Granted, this wasn't a kk, but, my old bge was in a cedar table, with a 1" piece of granite between the base of the grill and the table. When I sold the set up to make room for little boy, I found that the table under the granite was significantly charred, to the point that it would have burned through eventually. I'm just saying that the bottoms get hotter than you might realize, so be careful.
Robert