The Integra 9.9 is not a receiver but a processor while the Denon 4310 is a true receiver with a 130w/ch amplifier section.
I have an Onkyo Pro PR-SC885P (same as the Integra 9.8) which is the predecessor to the 9.9. It is an outstanding unit for the money. My son-in-law has a Denon 4308 (predecessor to the 4310) and it is a nice receiver, but I would go for the Integra 9.9 if you have good quality external amplifiers and the associated interconnects to connect them.
I had a Onkyo 805 receiver prior to the PR-SC885P and it did run very hot. The PR-SC885P run considerably cooler since it does not include the amplifier section. If heat is a concern for the Integra, just buy cooling fans off of ebay for about $30 that run quietly and plug into the switched AC outlet on the back of the processor. That's what I did and it effectively dissipated the heat on the 805 and now on the PR-SC885P.
Good luck.