Neat colour!
^n00b hit it on the head, they prefer warmer water, and will be more active with the warm water, but they can survive with water a bit cooler.
All my bigger betta tanks have a heater, and I keep them at about 80*F. My small tank has a heater too, and it's at about 78*F.
Though I'd never put a betta with a turtle. I think that slow moving, long flowing tail would be too much for even the most docile turtle to resist, and soon there'd be nothing left of the betta
Sir Max - I know responsible fish brokers ship their fish in bags with 1/3 water and 2/3 air. I know it looks horrible, but the fish needs the oxygen. I know it's shocking to see bettas when they first get shipped in, with basically just enough water to cover their bodies, but keep in mind that this should only be temporary, most fish are shipped with overnight delivery and are in the bags 24 hours or less (hopefully!).