If you have an Athlon XP 2600+ then you have one from 2003ish, if its an Athlon 64 2600+ @ 1.6Ghz then its from 2007, either way it is rather old.
Since you are rebooting every time the computer gets hot i would bet that either the heatsink/fan is clogged/jammed(most likely), the motherboard chipset is overheating, or the PSU can't handle sustained power output at those levels anymore.
Does it happen when you start up something intense or does it take a few minutes before it restarts? If it happens immediately i'd bet on the PSU, if it takes some time i'd bet on overheating and give everything a thorough dusting, changing the thermal paste will only do so much.