Any amplifier is going to need ventilation, but I’ve never had a problem with heat from mine. Also, go to their web site & get the dimensions - it’s a beast. As for receivers, you would do better with a pre-amp, but to get one with all the latest features would be very expensive. If you do go with a receiver, since the amp will be powering your speakers don’t feel like you need to get the beefier receiver. Get the least expensive model that offers pre-outs and gives you the latest surround decoding.
Another option (which is what I do) is buy an older used pre-amp & a Blu-Ray player, like the Panasonic BD80 which decodes everything internally and outputs via RCA analog which you then plug into the pre-amp. This will give you better sound quality than a receiver and still allow for all the surround sound codecs.