3.9 A * 120 V = 468 W, a pretty good amount of power to waste.
The power amps have some idle (standing) current, but a lot of the internal analog and digital processing circuits are also running and contributing to that power drain. The hottest part of my AVR is usually over the DSP, not the power amps.
I have seen standby, off, and on, and some AVRs with programmable sleep timers, but none with auto on/standby/off. I have by no means checked out all AVRs, however, especially for that feature.
Maybe you should consider a lifestyle change, or a job that allows you to sleep more regularly?
"After silence, that which best expresses the inexpressible, is music" - Aldous Huxley