This is against BOCCA code and can cause you big problems should you have a fire or when you go to see the house! Garages are not allowed to be tied into your existing home forced air heating systems.
If you would eliminate the garage doors then you can do this!
The reason this is NOT allowed, because when the HVAC unit is off, not supplying positive pressure to the garage area, then fumes can go into the duct work, into the house (living space) and cause harm to people in the house.
The solution, remove the garage door, frame in the opening with wood studs, use some type of insulation board on the outside then cover with exterior siding, add fiberglass insulation to the wall cavity, cover the interior with 1/2" drywall, texture and paint, now you can extend the duct work from in the house to heat and cool the additional living space.
Another suggestion, when framing in the garage door opening, frame in an opening for either a 3'-0" x 6'-8" exterior door or a 6'-0" x 6'-8" double door (better), and then you have access to move materials ad equipment in and out of your new shop area.