And you know he'll be OK with it, as that's not uncommon living conditions for bettas anyway.
Strikh, since you're new here, I won't give you a long ranting response (you can see that on many other threads).
FYI--unheated tanks are NOT ideal and the rice paddies bettas originate in are NOT shallow and NOT small.
As for what to put in the
QT tank, I know someone does keep a betta in there. Why do you want to keep the
QT tank running? Anytime you use meds to treat fungal/bacterial/ich problems, you will loose the good bacteria and have to recycle the tank. You can keep a sponge for the
QT filter in your large tank and let it colonize the bacteria and transfer it to your
QT tank when needed.