As long as it's a supplementary system to your furnace you shouldn't have any problems. They're only good to a little below freezing. As long as you're not getting a goodman it should be reliable.
the 7 and 7+ are faster (somewhat)
the 7+ has the dual camera (why I got it)
both have bigger screens
you get to buy all new accessories
moar
MOAR
MMOOAARR
seriously tho, if I hadn't already had a 6S+ I'd have an SE now. Once I switched to the bigger screen, I couldn't go back.
No opinion on the sound quality, but the SE is a great phone. I got my wife one last year.
I'm guessing with the issues you're having with the 5 it's related to Apple's security/parts authenticity checking.