A thermal management system or method may include features for pumping heat in a composite semiconductor structure. A heat pump such as a peltier device may be formed from compound semiconductor materials in a composite semiconductor structure. The heat pump may be thermally connected to an area of thermal interest such as a circuit device that generates heat during operation. The heat pump may also be connected to a non-compound semiconductor region of the composite semiconductor structure, which may be die bonded to a heat sink. Electricity may be conducted through the heat pump to move heat in a desired direction between the area of thermal interest and the non-compound semiconductor region. Plural heat pumps may be formed for cooling or heating an area of thermal interest in the composite semiconductor structure. If desired, control circuitry and a temperature sensor may be formed and used to regulate the temperature in the area of the thermal interest.