CPU Overhating

Hello TekSyndicate! Been enjoying the youtube channel of TekSyndicate since day one. Haven't been so active in the forums however, kind of stuck with lurking. Anyway, I'll get to the point.

I'm using an Intel i5 760 2.80GHz. After changing the broken stock fan with the Thermaltake Spinq Vt, everything was great, the temperatures were good. So I forgot about it and didn't check for quite a while. Just a few days ago I decided to check it and noticed the 90+ celsius while playing certain games. For all I know I could have been playing with these temperatures for the last 6 months. The idle CPU temperatures seem to be just fine, hanging around between 38 and 41, with an occasional jump to 43 celsius. The problems start when I try to play something. I tried playing F1 2013 and Civilization 5 and at both times the temperatures jumped up to 95 celsius. Playing games like League of Legends the CPU temp doesn't jump that high, but still remains at a uncomfortable ~87-90 degrees. I've changed the thermal paste just yesterday, got the dust out as well (compressed air), checked the BIOS whether the fan is on full (It was). The CPU is not overclocked. I have no idea what is causing the problem and what to do to remove it. I'm a little scared since I cannot afford a new CPU in case this one burns. Any sort of help/suggestions would be appreciated.

Well, the computer should shutdown or bluescreen if your CPU begins overheating.  However, 90c is getting pretty close to that range.

What program are you using to monitor temps?  Full specs would help as well.  I'm pretty sure that if you managed to pick up a Hyper 212 that your cooling problems would be solved.

I'm using a program called Core Temp.

Full specs would be:

Motherboard: H55M-LE
CPU: i5 760 2.8GHz
GPU: GeForce GTS 450
RAM: 4Gigs of stock RAM
PSU: Corsair VS550 550 watt.
I'm not sure what else I can add so please mention if I missed something I'l try to edit the post (not sure if it's possible to do so here)

CPUID HWmonitor seems to be a good temperature monitor from what I've heard and my experience with it. 

What is the voltage reading on your Power supply 12v rails, 5v rails? Do you have a multimeter?

Spikes or low drops in voltage from the PSu can cause inefficiencies on the board and increase temperatures.\

Also, are you sure the fan is running?