Waste heat from the magnetron (the thing that actually generates the microwaves) and its power supply. Typically, an "800 watt" microwave will require maybe double that power from the mains supply, i.e., 1600 Watts. Of this maybe 800 watts is delivered to the food as microwaves and the other 800 is waste heat, which has to be got rid of, hence a microwave usually has a blower inside to cool the magnetron and power supply.
If you have a micorwave with a display that is on all the time, this, and the electronics to run it, and the power supply to feed it, will be generating a small amount of heat, which may be enough to be noticed as a warm case.
Of course, if yours is a "combi" microwave, with a grill, then the grill will naturally be another source of heat, that will have to be managed as well.
Keep any air vents clear and maybe even vacuum them occasionally. Check for vents at the sides, bottom and round the back.
Trevor, February 2015
