PWM-driven MOSFET heats up
The 9 volts is a red herring. 0.13 volts across a FET of on-resistance of 0.05 ohms is a power of 340 mW and this will generate heat. The junction to ambient thermal resistance is typically 50 K/W, so without a heat sink and at a local ambient temperature of 30 °C, the temperature will rise to 30 °C + 0.34 W * 50 K/W = 47 °C then factor in that the temperature rise might locally increase ambient another twenty degrees and you are at 67 °C. Not really a problem.