A mini-split system would probably be your best bet, then you could also air condition it in the summer.
You'll want to do a little research and size it properly.
Up here at 3750 feet I think we used our AC in the house 2 or 3 days last year.
I may have to rethink the oil filled electric portable. My original thought was since this would be new construction it would be the time to build something into the room.
