It seems to feel much hotter when mine is flat, but putting it on the side seems to be cooler to the touch. Our system is in a cooled, vented media closet so no danger of knocking it over.
Mine is flat. I think it would have been cool for Apple to provide some supports to officially store it vertically, but I don't have the space to do so.
I have it on it's side also. I haven't noticed any heat problems yet. I did pick up some fan units for that side of the entertainment center. My dvr freaking runs hot, very hot!