Need help with possible overheating

[iRambL]

So some of the threads I've seen I'm going to try but I'll start up with the story of what's been happening.
About 2 weeks ago I started to receive stuttering in games. I would run at 60 fps or more then drop to 20 for a second then back up, and would continue every few seconds that way.
Specs
I5 4570 / gtx 770 / 750 PSU / Asus mobile (can't think of model) / 8gb ram / h60 corsair's cooler / corsair's case

When I started getting the drops I first considered software with new drivers and finally reinstalling Windows 10 which made my games run fine until I started my PC the next day and got the fps drops again. When opening my PC last night I noticed that my h60 pipes were running extremely hot and speed fan indicated that my core 0-3 temps were running at 88c and the same temp when I looked at the CPU in the Bios. PC has never blue screened or shut down on me just the fps stuttering.
Could my fps be caused by the overheating from my cpu? If so I can do thermal paste or even go get a new h60 since I've been running this one for nearly 2 years and nothing else on the PC seems do be running incorrectly. Would like some advice because I would rather fix it myself than take it in for repair.

Thanks for any help.

 

[hiyabusared]

88c is a tad hot I would suspect highly that the h60 has failed. I do not think reapplying thermal paste will fix the issue BUT it's not a bad idea to try and see. But if it were me I would just get a new h60 or maybe go to the h80i gt or the h80i v2. I know its a higher price but if you can fit it go for it.

 

[iRambL]

How do I check if the pump is not working?

 

[hiyabusared]

You can put a couple fingers on the pump which is attached to the cpu if you don't feel a slight pulse or vibration its a strong indication its failed. But best way is a stethoscope.

 

[iRambL]

Is there a way to see if the pump is operating in the Bios? Also would anything else cause that stutter since my GPU and ram both seem to be operating just fine?

 

[iRambL]

So I guess my cpu was pretty fortunate when I discovered this when I pulled off my cooler. You were right about the failure. Curious to see if I can rma it since these things have a 5 year warranty.
https://imageshack.com/i/pmO7GqIXj