The cheese will just burn a bit on the oven floor and do no harm. I would clean it up though after the oven cools down a bit or it will become baked on with further use and very hard to remove.
A very tasty way of cooking them is to cook on the BBQ. Turn them frequently and at the same time baste them with BBQ sauce. Set the BBQ medium to high and they should take about 10 mins. It really depends on if you like your meat rare or well done.
