MOSFET High Side conducts when low side switches in H bridge circuit
My guess would be that whatever drives the gate of Q1 has some capacitance, tending to keep it from changing voltage suddenly.  Thus, when Q3 is turned on, the source is pulled to ground while the gate is still idling at 12V momentarily.  The gate gets pulled low, but only after you observe some shoot-through, and since this occurs on each PWM cycle, it will heat up a bit.

I'd say take that 10K from the base of Q1 to ground instead of the emitter, but I couldn't easily find a spec to determine whether it will take -12V Vgs.  If not, a small capacitor between the gate and source would be my second preference.