No doubt one could look it up, and no doubt this is stupid question, but it just now occurred to me: What does being grateful have to do with a grate?

Being grateful has more to do with grace. The Latin term gratia means 'grace, charm; thanks, service'. Gratias agere 'to give thanks'. English grate < Med. Latin grata < Latin cratis 'wickerwork; harrow'. Not really the same thing.

Gratias tibi, Zmj!