I leave my two units on all the time. Although, mine are situated in an open, well ventilated space, so heat is not an issue at all for me. Even so, it's probably fine to leave them 24/7 set to "on" in a cabinet. When not driving them hard of course. At moderate settings, or when in "standby" mode, they generate very little heat. With regards to the trigger, there are three trigger mode settings on the back. The toggle switch is labeled: "Off", "Music", and "12V". I leave mine on "Music", allowing signal to trigger the unit, since my preamp does not have a proper 12V trigger out. It works fairly well, although sometimes at quite low settings the trigger takes a while to turn the unit back into active mode once it goes to standby. In that case, I just turn the volume up for a second and it triggers, then I can put it back down to my desired volume.
Also of note, at quite low input levels, the 2220s can go into standby mode while receiving low/no volume signal from your preamp. That could be a concern with surround sound channels while watching a movie with long, quiet segments.