Existing thermal management systems for microprocessors assume that the thermal resistance of the heat-sink is constant and that the objective of the cooling system is simply to avoid thermal emergencies. But in fact the thermal resistance of the usual forced-convection heat-sink is inversely proportional to the fan speed, and a more rational objective is to minimize the total power consumption of both processor and cooling system. Our new method of dynamic thermal management uses both the fan speed and the voltage/frequency of the microprocessor as control variables. Experiments show that tracking the energy-optimal steady-state temperature can saves up to 17.6% of the overall energy, when compared with a conventional approach that merely avoids over-heating.