Actually water temperature will naturally run lower than air temerature. It shouldn't be too hard to keep it at around 70' even if the room is warmer. As a test fill a glass glass with water and check the temp after a few hours. If it's where you want to be you're in business...if not you can run a fan across the water and it will help it a few degrees. Also be sure to include a filter that will create air bubbles in the water to help keep it oxygenated.
A 20gal tank should be okay, but a 30 would be better. If it grows much you'll have to get one later anyway. A bigger tank provides them with more freedom, and should you decide to add another one later you'll be set already too.
Good luck. Be sure to do the research on the species you want and get it's home set up BEFORE you bring it home. You'll both be a lot happier.