1. Put a dual-fan (4") on the top rear right corner (from the front), and connect it to the A/C inlet on the rear of your 875.
2. If your speakers are 4ohm loads, set your 875 for 4ohm loads.
If not, leave it at the default position of 6ohms (page 45 of your manual).
3. To help reduce power consumption while on Standby, disable the "Control", "Power Control" and "TV Control", from the Advanced Setup features (page 99 & 100 of your manual).
4. For better performance in the video output, turn the "Immediate Display" OFF (page 97 of your manual).
5. You can also disable the "Lip Sync" and "xvYCC" features from the Advanced Setup (page 99 of your manual).
6. Leave at least 4 inches (6" preferably) in top of your 875 for proper ventilation, and leave the front and the rear of your 875 on the open (not closed in cabinet).
7. Put your 875 on the very bottom of your rack.
8. Listen to Music & Movies at reasonable volume levels (not defeaning levels).
9. Turn down the heat during the winter in your home theater room, and use your 875 as the one that take care of warming your room. You'll save money in your electrical bill during winter.
10. It's true that the 875 (and 805, 905, 876 & 906) runs hot, but it is normal in their operation, because they have huge power supplies and they just don't have the space to have more heat sinks. Many separate amplifiers and other receivers, like some Denon and Yamaha models, also run hot.
* The 875 is a great receiver, enjoy it.
Bob