It usually varies between
CPU types, but the general operating temperature of a socket 370 chip for example should remain below 85c. 85c is the limit for a lot of processors of this type, but some, such as an SECC2 (Slot 1) processor should remain below 75c.
The manufacturer of the processor or motherboard can give you exact figures, but if you find out what type of connection you have on your motherboard/processor, I can find out for you.