Why does my plate heat up in the microwave? (no water)?

I put a serving for one of a frozen cerole (which is in a small rectangular plastic container 10cm long/6cm wide/7cm deep) on a normal sized flat plate (in case of spills). I auto-defrost it, which takes the microwave about 7 or 8 minutes. Why, at the end of this, is the entire flat plate too hot to hold? Microwaves heat up water and there is no water in the plate. Obviously the bit of the plate with the plastic container on it would heat up a little from the heat from the plastic container... but I'm talking about the furthermost rim of the plate. How did that get hot?