Denon AVR3808CI or Onkyo TXSR875

[Rike255]

The manual says you need a full 8" above the receiver and 4" behind it. I also have a wood shelf for mine and I tested a few heights. I left it with about 5-6 inches above the receiver and there is plenty of room for the heat to dissipate so 8 is probably an over pre-caution.
Behind I made about a 3 inch gap but there's almost no heat coming out of the rear so I doubt you need to worry about that.
The top of the receiver does get fairly warm to the touch but that's completely normal.

When I had about 3 inches of space above the receiver it didn't get any hotter then it does now with 5 inches but I moved it just to be safe.

With only 9 inches of shelf room you won't have enough room for any receiver. The unit itself is 7 and a half inches tall. Oh and 22 wide is fine that's how wide my shelf is. That doesn't leave room for anything on the sides though as the reciever is 17" wide and 18" deep.