Do hot entrees damage silver platters?

Silver platters are not damaged by hot food, at least not from the standpoint of their chemical nature.

Sterling silver is a mixture of silver and trace copper, with 92.5% silver and 7.5% other metals, usually copper. Its melting point is 1763°F, well over the boiling point of water or the temperature of food during cooking. Food and its vapors also do not chemically interact with silver in any significant way.