Yes you absolutely WILL need 2 t-stats!! Unless your current t-stat operates dual zones. An RHP must be on a t-stat just like your UTH.
For a 12-18" high enclosure, I'd be worried that an 80 watt will put out too much for you - but on the other hand, your room temps are only 60 so I dunno... I would say, use a 40 watt if you are using it WITH a UTH, but an 80 would probably be good if your using it by itself (on a t-stat).