From what I can tell, the Heater fuse goes to A/C system and rear window defogger. The compressor clutch is controlled by a relay. It may be possible to pull the A/C clutch relay (MG CLT). The relay might be located in the engine compartment relay box (plastic box) on the drivers side next to the inner fender wheel. The relay may be labeled or look on the inside of the top of the box for info.
Do not have an Avalon wiring diagram, suggest using the Generation 4 Camry (with V6) with the automatic A/C system. The two cars are almost the same.
Might be the clutch has a short or the compressor has a problem. Or maybe a relay has a problem. You can also download info on the A/C system.
If you can't find the Gen 4 data, try the Gen 3 wiring info.
http://oregonstate.edu/~tongt/camry
Or try the library, the often have manuals.
10 amps is a lot, not sure the dash switch would cause this unless a wire came off and caused a direct short. The system components that draw a lot of current are controlled by relays.
Suggest you try operating eveything except the A/C to make sure the heater motor, air control doors, etc are working. The fuse goes to more then one A/C circuit and also goes to the A/C control module that controls the temperature requlation in the car.