First, microwaves only heat up certain types of materials and its effectiveness varies. I have largely the opposite result: the plate is fine and the food is reasonably warm/hot. Water is one of the things it will heat up, which is good since it's common in foods. Interestingly it performs worse with ice, which is a problem for frozen foods.

Second, the microwave effect inside has hot-spots and cold spots. A microwave is basically a high power radio wave generator and the effects of waves cancelling each other out and amplifying each other come into play inside. It's why there is a turntable at the bottom of most microwaves: to keep the food moving around so that no one spot stays in a hotspot or a coldspot. But right at the center of said turntable doesn't actually move.

These combine to make frozen foods in microwaves pretty bad. Lucky hotspots are prone to have little pockets of ice melt into water, which then heats up more rapidly since water reacts better to the microwave in general. This is why you're instructed to take it out and stir. Microwave's doing a crap job and needs help.

Your plate doesn't normally get hot, but if a hotspot is touching the plate, heat will spread normally.