Most likely, you have not mounted the cooler well.
A common mistake is to use too much paste. The purpose of the paste is to fill in microscopic pits in the mating surfaces.. No more.
If you use too much, it acts like an insulator. It is hard to use too little. A small bb sized dollop in the center is all that is needed. It will spread by itself.
To mount the Intel stock cooler properly, place the motherboard on top of the foam or cardboard backing that was packed with it.
The stock cooler will come with paste pre applied, it looks like three grey strips. Do not try to reuse the paste. Clean the surfaces with denatured alcohol and a lint free coffee filter.
The 4 push pins should come in the proper position for installation, that is with the pins rotated in the direction of the arrow,(counter clockwise) as far as they can go. Since you have removed the cooler, play with the pins so you understand how they work.
Place the cooler so that all 4 pins are oriented over the holes in the motherboard.
The trick to getting it on is to push down on a diagonal pair of pins at the same time. Then the other pair.
If you do them one at a time, you will not get the cooler on straight.
Lastly, look at the back of the motherboard to verify that all 4 pins are equally through the motherboard, and that the cooler is on firmly.
This last step must be done, which is why the motherboard must be out of the case to do the job.
It is possible to mount the cooler with the motherboard mounted in the case, but you can then never be certain that the push pins are inserted properly.
If you should need to remove the cooler, turn the pins clockwise to unlock them. You will need to clean off the old paste and reapply new if you ever take the cooler off.
All motherboards I know of have a 3/4 pin cpu fan header. Use it. If the header is not populated, the motherboard will think you have no fan and severly downclock your cpu, and perfaps refuse to run.