A three Kg grill pan heated in the oven to 250 °C charred the surface of a cork table mat. A baking sheet heated to the same temperature left no impact at all. A dinner plate would probably not be heated to that temperature, and while it weighs in between the grill pan and the baking sheet, it should not have an effect on wood.

Wood has a flash point of 300 °C, so if there are to be candles together with plates at that temperature set on the table, then perhaps dishes for flambéing should be considered. Many oils have lower flash points.

Back in the 70s filet steak on an oak board and cooked in the oven was quite en vouge in Sweden. Over time the wood developed a nice dark patina …

In summary: I believe that table mats without finish will do fine.