So it reboots even when in the Bios? I guess it's probably a motherboard problem.
You said the temp registered in the bios is 37deg? What temp is that? Please post both the cpu and motherboard/system temp. Also, discharge your hands on your PC's metal case, then switch the PC on and physically touch each component in your PC. Let me know which parts feel rather hot. If you think there's a cooling problem, then remove your PC's side panel, take a strong house fan and let it blow into your PC while it's on. I doubt it's a problem with heat though.
You said you upgraded your PSU? Which model are you using at the moment, and which model were you using before? There's the possibility that your upgraded PSU is faulty, although I highly doubt it. I still think it's a motherboard problem.
Reset the CMOS settings (use the jumper next to motherboard battery) then try again.
Reduce the CPU clockrate or "FSB" (called something else on corei3 motherboards) to the lowest speed that your PC boots/POSTs with.