How to match up heatsink-fans to a CPU?       
   or why in the world does not Heatsink fail to work fit or overheat.

These are the  key features to address: (see the purpose of a HS)
  • Fits and does not bend over local capacitors. or hit  DDR RAM or other motherboard parts (MoBo) Some monster wide or too tall HS do not fit, (HS = Heat sink)
  • Matches Socket size type , AMD or Intel  (and CPU class)  (It is true I do like real  screw mounts)
  • Wattage ratings, some are 50watt rated and and many are 95watt.  (  even larger are sold too for gaming systems) (A high wattage HS always works better, if it fits)
  • Fan connector 3 pin or 4 pin and if Intel or AMD type or universal.  There is no standard pinouts. (each OEM is different) A DELL PC will compain (F1 error) if RPM from tachometer reads wrong ! (adators are sold)
  • The sockets that use real screws , have USA #6-32 screws or 4mm (.7p) metric, be sure to match this. (and the under MOBO mount with nutserts need to match that too.)   or 3mm (.5p)? is also common!
  • The TIM needs to be good quality , A.K.A. heat sink grease. (maker Shin Etsu is the best)
  • Not so tall or the case lid can not be closed.  (but no lie, big is best for longest life of the CPU)
  • See FAN PIN-OUTS here.
  • If really super serious about heat sink mounts the place to go is here @ NOCTUA.  or this  popular mount by them.

First lets do Intel mounts , both screw type or snap in mounts.    SOCKETS MATTER FIRST learning what you have first.
To quote the wiki:
For LGA 775 the distance between the four screw holes for the heatsink is 72 mm, thus such are not interchangeable with ones for sockets LGA 1156, 1155, 1150, 1151, which have a distance of 75 mm.
This is steel Mobo back mount and is very strong. (both metric and #6-32 screw types are used) The beast mounts are metal, some plastic are ok.

This first fan heat sink below is very good, and has snap pins that are adjustable for many (5) Intel CPU, this is a PRIME part to buy if you like snaps. 
Most Intel fans-HS, seen sold  are not like this , the fan only fits 1 in 5 CPU sockets by Intel. (no flex adjusters present)
The below INTEL fan works great, if watt rating is enough is best for fitting most Intel CPU made. The below is 50-65 watt and no good for 95 watt or 130 watt CPU, buy one with deeper HS fins.
My joke is Intel invented this weak snap solution to justify BTX nightmare cures. 
The Plastic Rivets below must be pushed down to lock the tips and pulled back to unlock the tops, the cams on top are 90degree and CCW is unlocking the cam. (like Intel instructs you clear as day)
Do not turn on  the PC until the HS bottom is tight and fast to the CPU top, not floating about, if is floating there , you did it wrong.
This Rivets are very very old how they work, take your time. (it has no spring (sadly) but uses cheezy ratchets) They do work but they are fiddly and funky in all respects doing service, I slow down to x10 speed and super careful.

Here is my HP  Wx4600 PC, fan, LGA775 Core 2. (one of the best fan/HS made)
Note the Imperial inches screws #6-32,  not metric,  My most favorite is here, for testing.  I also use this on my Intel D945G motherboard P4-HT-651 !
The springs do all the tension here,  when turned and the bosses below bottom out that is all you do, and the springs do the job , there is no need worry tension here ever.

The Below is an AMD solutions,  a clip on HS. with custom base, all very good.

The below adapators all you to converet your MOBO to use universal China Alien fan/heatsinks.  Very common now, this.

Same thing here but far better metric screw mounts.   The below base mount , is adjustable wiht the yellow wings. M3 screws there only.

cpu base bracket desktop 775 up to 1366 (adjusts)
The next 2 photos are very hard to get with sizes stated, here they are and they are  M3.  27mm long.  The springs are calibrated to meet , Intel compression on the socket pins of CPU,  is controlled by spring types.
The screws have stops and the spring tension is set by those stops, so the screw must match the SOCKET you have (775 to 1366) and must match the HEAT sink base offset design. (a match all, do not mix these up)

Below is what I use on my Dell 3020, the deep fan from DELL is for the higher wattage CPU and far faster CPU.  I think nothing beats this solution for strength.
My photo shows the vast differences.  and #6-32 screws. (Imperial USA screws) not metic. (means will not fit the above China custom metric mounts.)

Last of all is mostly a bad IDEA, BTX. (the still birth of BTX failed)
BTX PC's should be avoided. (if you want to upgrade later BTX is failure)
They all have very odd/Queer mounting,  (custom BTX parts end to end not at all complatible to ATX robust diverse solutions.)

Here is the BTX horror seen on many DELLs  Optiplex 380 below,  the left side below fits only the Dell hinged mount (right photo)
BTX is basically a Dead product now, see the Intel spec on it here.  (the BTX fan does have better cooling to CPU HS and the CPU heat sink can be massively heavy) Intel makes 165watt CPUs now.
In theory BTX might have less fan noise. (using the dream no other case fans needed for other chips and PGU cards on board) << this is really bogus  as we have very big slow quiet fans now and spin up as needed.
The shroud uses the case fan only, and that is problem #2 and ATX solutions do not work here. (vast and diverse for ATX) The BTX all these parts are married (case+mobo+HS+shroud+fan)
But that hinge part is easy to find ,but oh boy the  other end on the right only fits in to 2 holes in the PC main BTX chassic bottom , so do  not buy naked used BTX motherboards for these Dells:
Optiplex, XPS and Dimension numbers, 755,780,380,760,3100-e310,3100,5150,9100,9150,9200, xps 200s/210/310/400/410/420/700/720, E520, E310, at the least. (only Dell went BTX hog wild !)
NOTE the sideways 45degree twisted CPU MoBo , seen and to avoid. (clue 1 is that)  Sold for $15 on fleabay are junk, IMO. But a Dell 3200 PC or mobo is great.

The purpose of the Heat sink and fan are to capture all wasted heat from the CPU and expel that to the outside of the PC casings, if the case fans are dead, this job will fail.
If the CPU gets too hot , the intel inside (brains) will slow the PC down, and at 90C+ shuts the PC off.
The more wattage the HS is rated for the cooler it runs and the longer the CPU lasts !   The HS large is needed to play Far Cry 5, Metro Exodus, or Deus Ex (MD) full tilt. (never reading your email)

If you are in India, learn that the word CPU, does not mean PC nor Computer, the CPU is a U.S.A Intel invention, use the term  correctly please.
The below needs a  165Watt  heat sink or better.  Yah  HOT.
LGA 1151 socket,  This CPU can keep a basement warm ! (to go fast you must burn heat, until mankind invents the true SU:PER CONDUCTOR ,  this loss is called Entropy. (just like your car and that hot engine radiator wasted heat)

A CPU only burns power on demand (yours) for sure AAA+ $60+ games) but running just windows desktop the whole PC may only need 20watts to do just that. (by Design !) and far less in sleep mode.

FAN PIN-OUTS:  (ask your OEM maker first or RTM read the manual, if you have Asus , Gigabyte or MSI , MoBo, then  this information is 100% for sure in the manual. ( has for 25 years running)
There is no  fan standard wiring, No ATX spec. (Intel , Dell and HP and China clones all  do what the want for this) And RPM monitors in the BIOS are not the same, either (by OEM)
If you wire it up wrong and short  +12vdc top ground(gnd) the mobo burns up or the PSU shuts down, toss coin,  never do that.
The beauty of 4 wire fans is the BIOS can even run the fan at 300RPM super duper quiet.

On ebay they sell adapters for fans wired up in vast different ways, to match fan maker to your OEM PC.
Intel fan pinout. This also works for my HP Wx4600 seen above. This also work on my Intel D945G based MoBo.

AMD is below:

My P4A78 mobo, AMD Phenom II uses this same pinout.! noticed the key, do not force the plug on backwards.

This is a generic pinout and common 3 pin fan. (not smart like the above ) a real loud screaming fan.
I use   at least one case fan, on the front of PC, that is 120mm diameter and 4 wired pins and runs slow when PC is cool. (buy a fan that supports slows speeds, and has a low noise spec. )
Buy only a Mobo that has only 4 pin fan jacks, (all ).
Also some better GPU cards have there own and far better noise spec.'s and run slow when not hot. ( you pay more and you get more...)

Never do's:  (do not overheat any PC)
Never Drill or cut or file any motherboard ever, they are complex and dense  multilayer boards and if you do , the MOBO is now useless. (or worse just blew up that $900 CPU above.(i9-99xx)
Never drill a PC case with out using vacuum cleaner at the same time, or removing all electronics from the case first.  Metal filings and electronics, are not good to be mixed ever.
Never run any CPU with no HS at all,  (or its fan disconnected unless doing a fan noise check for say 15 seconds only)
The fans speeds up as the CPU gets too hot, BY DESIGN, do not try to stop that from happening OK?  (a modern PC has BIOS that regulates fans for the least noise and most effective heat control)
A cool PC does in fact last longer !
My Asus prime Z270 the fan profile can be edited,  to what ever floats your boat. (even silent until CPU hits 35C or ?) (some fans have a minimum speed of 300RPM, but makes no sound at all that slow)

version 1.  10-29-2019