Some plates get hot in microwaves, and shouldn't be used in them. Other plates don't absorb microwaves and stay cool.

The difference is mainly in the type of clay used to make the ceramic plates (there's also some types of plastic that shouldn't be used in microwaves, but that's another topic). Clays that contain a lot of iron oxide, which tends to make for a dark reddish-brown colour though that may be covered by glaze, are especially bad for microwaving. Plates made from such clay can get very hot, and in the process they absorb a lot of the microwave energy instead of letting it go into the food. Hence, the food doesn't warm up as much as you expect.

Microwaves sort of bounce around inside the oven, reflecting off the metal walls, until they hit something that absorb them. That something then gets heated up. Glass and some types of ceramic (porcelain) are transparent to microwaves, just like glass is transparent to visible light. So if the microwave hits such a plate, it just goes right through and bounces off the oven floor. That wave then has a good chance to hit the food.

Plates made from red clay with lots of iron oxide, or that are glazed with some color made with a lot of metal or metal oxides, are opaque to microwaves and absorb them much like black paint is opaque to visual light and absorbs it. If a microwave hits such a plate, it gets absorbed and heats the plate instead of having a chance to heat the food.

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.

For the same reason a bicycle tire pump gets hot when you press the handle down. The molecules bounce off the outside layer the hardest. The pump uses air molecules and microwave uses water molecules. Imagine a tennis ball going through the air. It is loosing momentum to heat and drag. But when it hits the wall most of that energy is changed all at once and it doesn't bounce back near as hard. But you can add energy by hitting it again. If you could speed this up and hit all the area of the wall over and over the wall would get hotter than the air between you and the wall.

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Due to its porous nature and water content, clay heats up. The glaze is never perfect and contains numerous microcracks that allow bacteria and other contaminants to enter.

The same can be said for wooden cutting boards. If you put one in the microwave, it will become hot.

Because the porosity breeds fungus spores of all kinds, both are extremely unsanitary to use.

Pyrex glass containers are my recommendation. They always work perfectly, and you can simply cover the leftovers and store them in the refrigerator at any time.

Porcelain is porous.

If it has an unfinished edge which many do on the bottom, water gets into the dish and the water heats up within the dish itself making it hot.

Use glass in a microwave only.

Microwaves heat food by causing the water molecules in the food to become excited, thus banging into each other. That creates friction, which creates heat.

Objects heat up through the input of energy. Heat doesn't absorb cold, rather cold absorbs heat. Plates are typically made of some kind of stoneware, e.g. ceramic, which is clay.

Side note: Corelle dishes manufactured by Corning are glass and do not heat up on the microwave. I use Corelle for this reason.

The cold stoneware absorbs heat energy from the food. Because the food is losing heat to the plate it remains cooler. The water molecules continue to produce heat through friction that the plate continues to absorb.

I would imagine if the food were heated long enough to the point all of the water had evaporated the plate and the food would reach equilibrium. However, the food would long since become inedible if not combusted.