cpu i5 6500 false overheat

[mph101]

I've developed a problem the past couple days. i5 6500 skylake can't overclock, don't game. Nvida Geforce 960 gpu. The ASUS (mother) software and CPUID HW software show it over heating. But its not any heat coming off the fans which are clean. System is running normal , no indication of the cpu overheating. Programs and performance normal operation, no shut down, no blue screen no slow operation, task manager showing 21% cpu, 28% memory, voltage on the i5 is 0.736 jumps too 1.276 but average is about 0.736

Its not over heating. I know the pins are problem on the cheap intel heatsinks. When I pressed them earlier into the mb the temp dropped to 39 -43 C while surfing the web, using web cams, and VLC.
Currently I am showing 87 C with a motherboard temp of 29 C. The fans aren't even spinning on the gtx 960, its cool .
When I press down on the plastic pegs holding the cheap cooler down. Currently I am showing a cpu temp of 62 C but a few minutes ago it was 89 C.
This is a increasing problem because I can't boot up as the bios boot saying overheating error.

Suggestions please?

 

[Someone Somewhere]

Your CPU is overheating, because the heat can't get out of the CPU to the heatsink, and then to the air. This is why the air coming out feels cold.

It's not an issue with the GPU, so that feels cold too.

Check the plastic pegs are properly through the board and twisted into place.

If that doesn't work, buy a new LGA1151 compatible heatsink.

 

[mph101]

Thanks , I really appreciate your reply. Currently my i5 is running at 100C, likely it will die shortly. I have a phanteks Evolve case. This is the micro atx case, great case, solid. I was looking on amazon a air 1151 cooling BXTS15A would fit, the comments say it won't.
Man this is my third build its a yr old but nothing but hell hardware and windows 10 unlike my prior 2 windows 7 build. I think its time for apple I am tire of being a mechanic
...Or maybe a AMD bought production PC