Adding a closet will probably not make much different in the appraised value since you are not adding sq footage. You should check county records to see what sq footage your house shows. An appraiser can only use the sq footage that is on county records. If someone added on sq footage to a house without permits then the appraiser can not count that sq footage when determining value. If the workout room was added on without permits it will not matter if you run hvac to that room because the appraiser can not count it.
If the room is just missing heating to be considered finished sqft, your cheapest option might be to just add a cadet heater.
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