Do defrosting plates work in reverse?
Does heat transfer go both ways?   Generally yes, the conductivity of a material is the same if you reverse it and you could use a defrosting plate to cool hot food.   The plate would require good contact with the hot food to allow the heat to be conducted into the plate.   This heat would then be conducted through the whole plate area (larger than the contact area with the food) and dissipated by natural convection to the air.   If you've ever cooled a hot drink by putting a spoon in it, you'll get the idea.