Thermostat

Same wires, yes. Make sure it'll handle both heating and cooling (if that's what you need).

I have a Lux with a remote. Nothing like turning on the heat from bed. It's programmable but I've never done that.

The directions are pretty straightforward so it shouldn't be a big deal to install. Have your camera at the ready to take pictures of the old install before doing anything.. or write down what wires go where.