I recently upgraded my laundry room from an electric dryer to a gas dryer. The 30 amp circuit was left in place including the receptacle for for the dryer, which was very handy for the floor refinisher to just plug in to. Now that it is getting colder I would like to add a small electric baseboard heater and thermostat to keep the room warmer. I would like to tap the existing 30 amp circuit (my service box is full even if I didn't mind pulling the extra cable) for the heater, possibly by just running a 30 amp plug from the thermostat into the outlet.
The best way to tackle this issue is to remove the 30 amp plug and replace it with a junction box. Locate a sub-breaker box on the wall and feed it with 10-ga 2-wire +ground cable from the new junction box. With the sub-box you can create two or 3 circuits with different amp loads (15, 20, 30) and wire sizes. Be sure to enclose the feed and any load cables in conduit if they are exposed to the living area. And follow all safety rules, including shutting off the breaker at the main box while the work is ongoing.