I've had the Pioneer VSX-816 for about a month and exchanged it for the Onkyo TX-SR504 just this past week. My reasons:
The Pioneer wasn't bad, but for my small satellites (Polk RM6750s) the 816 made them sound tinny and not spacious enough for movies. Music, especially for my iPod, it sounded great, no complaints. I returned the Pioneer because I had issues right off the bat when using my component dvd player going in to it and then having no video to my tv. I read, rechecked and asked Pioneer themselves about why I can't get any video and no results so I had to connect it directly to my tv. Sure the 816 had more features but it's the sound quality that drove me to Onkyo.
First night I hook up the 504 and immediately the sound image from movies and music was a definite improvement. I like the warm, full sound compared to the brighter tones from the 816, but that's how I like my setup to be. I tested out certain scenes my favorite action movies and little ambient sounds from the left and right speaker were louder, clearer and more enveloping. I used both an SPL meter on both receivers so the auto setup feature of the 816 was nice, but it's not difficult not having the onscreen menu from the Onkyo. The remote on the Onkyo is much nicer and refined having less buttons than the tic tac sized 60+ buttons on the 816.
Another reason I knew this was the entry level receiver for me: it took my component input dvd player and had no problems using component out to my tv. Overall the 504 sounded better, was easier to hook up and even though it's rated lower in watts than the 816, it doesn't sound that way to me. Plus in my opinion, the 816 looked cheap compared to the 504.
Oh yeah, about the heat issue, doesn't bother me and have had no issues (yet) about the sound dropping off for no reason. Just make sure it has adequate ventilation and it'll be fine.