My house has a small room that was added on to the back of my attached garage. It's about 6 feet by 12 feet. There are two outside walls, one common wall to the house, and a common wall to the garage. When I moved in, I added R13 value insulation to three of the walls.
There's an HVAC vent on the interior wall and I also added a small electric strip heater, yet the room is constantly colder than the rest of the home. The insulation helped a bit, but not as much as I hoped. Any ideas?
This room is crying out for its own HVAC system. Often when rooms are added onto existing structures, the person constructing it thinks, "I have a duct, so I'm simply going to put a hole in the wall and add a register." But forced air systems don't just supply heated air - they're effective because they pull cool air back to the furnace to be reheated, too. I'm guessing you don't have return duct that does this, and the small heater you added is outpaced by the cold air.
This is a good opportunity to consider a split ductless system. I think it will give you you the amount of air conditioning and heat you need for this small space. Installing it will be less expensive than installing a central system, but isn't inexpensive. However, split ductless systems are very efficient, and often qualify for a variety of tax rebates and tax credits. Good luck!