How hot a receiver gets is mainly a function of the temperature of the air around the receiver, how much you are pushing it to drive the speakers (listening to loud volumes for long periods will use more power ~ more heat generated) and the air flow around the whole receiver. If the top doesn't have much room for ventilation and now you remove the feet, natural convetion can't take place through the top and bottom vents. When this happens, the temperature inside the case and the junction temperatures of the IC's will rise and potentially cause them to either not function properly or be permanently damaged.
There are only three ways for heat to be transfered, conduction, convection & radiation. In the case of the AVR, it is mostly convection with some radiation. Since there's no specific "cold-plate" to be the "heat sink", the thermal guys at Pioneer didn't use conduction as a method to get the heat out, and I wouldn't expect the outer case to get hot unless you have a serious problem. You really have to measure/record the temperature of the air escaping for period of time to fully understand if you potentially have a thermal issue.
Plus, natural convection is a function of gravity (among other things). The air enters the chassis from the bottom vents and the free-convection takes the heat out of the top vents. If the air vents weren't needed, Pioneer wouldn't have spent the $ to add a step during the manufacturing process to punch them in the case.