lukewarm dough right into the fridge?

I've made Saltie's Focaccia many times since this was posted. If your flour is at room temperature, the dough won't be that warm - maybe a touch warmer than room temperature, once it's all stirred, but only a small amount (and it's probably no warmer than if you were making it on a very hot day).

I never let the dough cool before putting it into the fridge. I've never had a problem with the dough affecting anything in my fridge - though I should mention that I always place the bowl with the dough in it as far away from the milk as possible, which is something I do anyway with any item that is room temperature going into the fridge. ;o)