How do I slow evaporation in my "tank"?

I only put tank in quotations because it's technically a kritter keeper.

I currently have my male EE betta in the medium KK from Petco but I'm contemplating getting one of the large ones so he has a bit more room. It is heated and I have a sponge filter in there for him.

I've noticed in the medium one, the water evaporates really quickly because the lid is basically open with all the little holes, and the warm water. Is there a way to keep the water from evaporating as quickly without hurting my boy?

On an only vaguely related note, his tank is currently bare bottom but I'm thinking about putting sand in the bottom. Is sand a bad idea with a sponge filter or a fish who seems to derive pleasure from biting himself?