I tested the MINIPA70 kit with a 13.2 V power supply, 0.2 W of input signal and 13.5 W of output signal. The temperature rises continuously to about 70 °C when I stopped. The current draw reached about 4.3 A.

The increasing current at a fixed gate bias is a sign of thermal runaway. The increased temperature lowers the gate threshold voltage, thus increasing the current flow through the drain, which further heats the MOSFET.