Several things:
1. Like said by someone before, run memtest86 - it is a program that tests your RAM for errors. I strongly doubt it is a RAM fault though, but its best to check anyways.
2. The 82C is definately NOT good, especially if you aren't even overclocking. I would suggest using a CPU stress tool such as prime95 (finding it through google should be no problem), whilest running a temperature monitor - I'd recommend speedfan.
If the temperature approaches anywhere near 90C, you are in trouble - the chances are your heatsink on the CPU isn't attached properly - this could be because the thermal paste is ancient, or it became dislodged, or dust etc. The right course of action then would be to reaply some thermal paste and correctly attach the cooler or remove any obvious dust clogs.
However, if the temperature isn't high, I would recommend you run prime for about an 2 hours and see if it gives you any errors. If it does, something in your system is unstable. If it doesn't, then it is more or less definately a software related issue.
To give you any further help, I'd appreciate if you posted your full system specs, - make of motherboard, RAM, etc, and also whether or not you are overclocking.