First thing I would check is dust. Either in the heatsink or the vents going into the case. That is usually about 80% or more of your heat problems.
No - he has NO case fans - Shut the PC down - that's first. Or get a desk fan blasting now. Then clean it out, and keep it clean. Note that all the dust does is "trap" the heat or block air flow so I think 80% is pretty high - but that does not take away the importance of keeping the system clean of dust - as WITHOUT A DOUBT, a dirty PC runs hotter than a clean one and a dirty PC can cause a PC to overheat.
@C_P - Note according the
Intel Thermal Specs for this processor (page 79) states the max case (that's the CPU die's case - not the PC case) is 76°C. You are playing with the thermal limits of the CPU. Also note that as a repair guy, I have seen CPUs fry - be warned that a burning hot CPU can literally melt and deform the socket and burn and deform the motherboard underneath - destroying the motherboard!
As far as software, many motherboard makers include a monitoring program with their motherboards. It is usually buried on the motherboard utilities disk and you have to look for it. Or check the motherboard maker's website for a current version.
Also, you might get an idea as to the correct temp by checking temps with your monitoring program, then quickly boot into the BIOS menu, navigate to PC Health and check temps there. They will be lower than your previous readings by 5 or so degrees because temps go down immediatly during shutdown and when the CPU is idle - or near idle as in the BIOS menu - that's why you have to be quick.