When I was checking out my sat deal sometime back, I noticed the same problem. I had the Directv box sitting on top of my video switch and the cabinet door open (sits on the right side of main tv), but after about an hour, the box shutdown, at first we didn't know what had happened but after 15 minutes, it fired back up again although it did it again shortly after. Apparently it has a thermal switch in it that keeps it from overheating.
When I do the permanent installation, I plan on putting in a small shelf on the right about halfway up in the cabinet. This way the box can sit by itself and hopefully will stay cool enough to function correctly.