Both AMD and Intel publish detailed information on the operating temperature ranges of their processors. Both companies refer to case temperature, which typically is measured in the middle of the processor heat spreader. As you can see in the tables below, an Athlon 64 X2 processor is designed to work at up to 78°C, while the Core 2 Duo may be operated at as much as 72°C. You will notice that the maximum case temperature (tcase) depends on the actual thermal design point that a processor is specified for: a TDP 35 W Athlon 64 X2 processor may reach a maximum of 78°C, while a 125 W TDP Athlon 64 FX must not exceed 63°C.
As a processor moves out of its thermal design range, there are countermeasures that can be activated either by the motherboard or the CPU itself. Typical platform action involves switching to maximum fan speeds while the processors fall back to their protective mechanisms.