I’m amazed that nobody pointed out some of the basics – clock cycles not used by any process are used by the System Idle Process. So to answer your question a Fox process using 100% of the available clock cycles should have zero effect on the temperature of the CPU - I would be more concerned about the adverse impact on other processes that might also be running.

That said, if you use Advanced Power Management (APM) and can find a way to suspend the PC and safely resume at the required moment then the CPU should run considerably cooler when in a suspended state. This in itself may be undesirable, because the daily (or more frequent) cycle of allowing the CPU to cool down and warm up will cause repeated contraction and expansion and eventually the possibility of metal fatigue. The generally accepted best practice to maximize the life of your component is to minimize temperature change and keep it at the lowest temperature possible.

Technologies like Intel’s Speed Step and the Transmeta Crusoe speed control will lower the operating temperature of the CPU but this is a byproduct of an attempt at extending (laptop) battery life not the life of the CPU.