Can I put heated flooring over it?

I recently bought a summer getaway home by a lake. It is a little worse for wear. My husband and I are both very handy people though. Our plan is to fix the little shack up and get it livable in a few months. The biggest issue is the floor. The floor is all different and partially ripped up. The previous homeowner died in the house. He was a bricklayer and was in the middle of laying bricks in the living room and bedroom. I don’t really know what to do. Do I continue with a brick floor? I don’t like how hard it feels on my feet and I hate to cover it with a rug. My kitchen and bedroom are just plywood right now. My husband came up with the idea of laying down heated flooring and then tile over top. Then we would have quit heating in the kitchen and bedroom during the winter. I am a bit hesitant to do this because I don’t want half my house to have good heating and the other half not. My husband doesn’t see the issue. There is an electric heater in the living room. He said that should be good enough. I think it would be weird to walk from heated flooring to cold brick in the winter. I am loosely thinking of calling a HVAC business and asking if I can set heated mats right on top of the brick and then do tile on that. It would add some height to the floors, but it would be worth it.