A wall heater is a single unit that sits inside the wall and forces hot air throughout the room with a fan. It's simple to install one because you don't have to do any new wiring. All the time in condo conversions, I've seen the labor crew hook the new wall heaters to the same wires that they disconnected from the old baseboard heaters. No need to replace the thermostat. No need to run new wire.
Here's what you'll need:
an electric drill
a circuit tester
a pry bar
Here's how you get started:
1. The first thing to do is to turn off the power to the baseboard heater. Never work with live wires. You may want to buy a circuit tester before getting started. They're about $10 and are worth the money. Or you can be safe and shut down the whole house. That's guaranteed.
2. The next thing is to remove the old baseboard heater. There are many ways to do this. Most often I see it done with a pry bar, though that scuffs up the walls pretty good when the screws holding the heater in are yanked out. Either way you'll have to patch those old holes a little bit.
3. Use your stud finder to locate the closest stud to where you want the heater to go. Keep in mind, it has to be in the same stud bay as the wires you'll hook it into. Once you've done this, mark a vertical line along the edge of the stud. That will be the edge of the wall heater. Trace an outline of the wall heater's back that will fit into the stud bay. Get your drywall saw and start cutting.
4. Once you've got a hole, do a test fit to make sure the hole is big enough. If so, connect the wires from the wall to the wires in the wall heater unit. White to white, black to black. Make sure the wire nuts are tight and don't leave any copper exposed. Make sure also you can't pull the wires apart easily.
5. Put the fan in the wall and screw it into the stud.
6. Turn on the power and turn up the thermostat to make sure it works. Then put on the trim plate and start enjoying your new heating system. Think about buying some gourmet hot chocolate to enjoy and don't feel guilty about splurging. You'll still end up on top with all the money you'll save on your electric bill anyway.