The heating effect you see in a tyre is down to a combination of factors, but the lower the pressure in the tyre, it has to deform more to put a greater area of tread in contact with the road. The deformation of the side walls is what causes the greatest wear and probably generates the biggest temperature rise of the tyre.
Conversely an over pressurised tyre will run cooler, but it also does not put down as much tread to road, so the blocks of tread will work harder and that might cause some heating.
Vehicle and tyre manufactures work in conjunction to establish the best compromise of tyre size and pressure for each type approved model, They consider things like changing load in the vehicle, but will also be aware of the work induced self heating of the tyre carcass,
Sticking to the car manufacturers recommended pressures represents the best compromise between grip, and wear both physical and thermal degradation.