Cube-1 is a heterogeneous multiprocessor consisting of 3D stacked chips connecting with inductive coupling through chip interface (TCI). The most important problem of Cube-1 is the thermal management. Unlike TSV which can be used for heat dissipation, stacked chips are electrically contactless in inductive coupling TCI. First, by measuring the relationship between the chip temperature and leakage monitor, we examined that the leakage monitor can be used as a temperature sensor of the chip. Then, we measured the thermal characteristics of Cube-1 by leakage moniters. The chip temperature change due to the internal power was evaluated, and it appeared that the chip temperature was not changed with this level of power consumption even if the chip was sandwiched with other chips. The heat conductance through the stacked chip was also evaluated. Evaluation results show that the heat dissipation of the chip sandwiched with other chips is almost the same as that of the chip placed top on the stack. Finally, we proposed the supply voltage control system of the stacked chip by making the best use of the chip temperature data from the leakage monitor. By using the proposed control, the energy efficiency can be improved by 5% at maximum.