As the resident noob im gonna go on a limb and try to answer. From what i've read, you don't even need the AP hooked up once you install the new tune. Once it's in the CPU, it's in. Perhaps it could get so cold/hot that when you hook up the AP it wouldn't work but that could happen to anything no? The car CPU, our phones, ect. I don't think you should worry about this issue. With that said i wouldn't leave it in a hot car in the sun, same with phones ect.
Like any electronic device I wouldn't leave it in plain view in the car or in the sun. When I'm parked I put a hat covering mine just in case. If I'm in a sketchy area I move it to the glove box or take it inside with me - only for extreme cases though like if I parked it at an airport and left it in parking. But most of the time it stays hooked up on my A-pillar.
If you load the tune yes the AP is no longer needed until you change the tune out but in my opinion you're losing the best parts of the device. You can do so many things with it - log times, log data, monitor hundreds of parameters...launch control, traction control, monitor estimated HP and TQ, fuel level, and probably tons more I don't know about...scrolling through the parameters to see what this device can actually tell you is mind boggling. Having the AP in view is part of it's usefulness so I'd be sad to hear someone loaded their tunes and then unhooked it, they'd be missing out on all the fun.