The first thing you need to do is make sure you have a problem.
Electric furnaces use heating elements similar to electric ovens. The elements extend into the air stream passing through the furnace from wiring connections in the wiring compartment. If you open up the wiring compartment, you can see the ends of the elements where wires connect to provide 240 volt current to the elements. It would be easy to check for 240 volts across the element terminals with a voltage meter, but checking is not safe for a person not familiar with electrical wiring.
If you are not knowledgeable about electric wiring and do not have a voltage testing device, I suggest you check to be sure the element is actually still getting power (and generating heat) by using your electric service meter.
If you turn off all the circuit breakers in your electrical panel, the meter will stop turning. Check to be sure it does. Next, turn on only the circuit breaker(s) for the electric furnace. The meter may turn very slowly since a transformer in the furnace uses current to power the thermostat. If it starts turning quickly, you may have an element using power right then.
Turn up the thermostat and run the furnace through a heating cycle. Check the meter speed while it is running. The elements in an electric furnace are typically 5,000 watts each. This means they use 5,000 watts of electricity every hour they are on. The number of elements in your furnace depends on the size of your home. Your furnace could have from two to five elements.
Turn the thermostat down to stop the furnace cycle. If the meter drops back to a very slow rate of rotation, it is likely you are feeling residual heat from the elements rather than heat being generated by an element that remains on after the furnace shuts down.
If your meter turns at a rate that would advance it 5,000 watts in an hour with nothing but the furnace breaker turned on at the electrical panel, you have an element in the furnace that is not shutting off.
Another safe way to check for an element not shutting off would be turn the thermostat way down or even off overnight. It is winter, so that may not be practical. If you can turn the furnace off overnight, any residual heat will be gone in the morning unless, as you suspect, there is an element on when the furnace is off.
I don't suggest you attempt to check for voltage at the element connections inside the furnace yourself. Power would have to be turned on to the furnace after you open up the wiring compartment. This exposes live connections with high amperage disconnects that are dangerous if you are not familiar with electrical wiring.
If you determine that one of your heating elements is remaining on, you should be sure the person you call for repairs is familiar with Coleman furnaces. A good repair service person should carry replacement parts with him so he doesn't have to charge you for more than one trip to the house.
If you have any questions about these suggestions, please ask.
Loren
lw@buyerbewareinc.com