Is $1,950 to add insulation and inject foam in walk-in closet a fair price?

I am looking for advice on making my primary closet more temperate. In the summer it gets extremely hot, and in the dead of winter ice will form at the electrical outlets/corner of the finished interior drywall space. The space was added by the previous owner to a 'bonus' area above the garage which is not heated/cooled. There are no registers in the closet; the only conditioned air it receives is from the flow through the master bedroom. I believe it should definitely have a dedicated vent given its size. Instinctively, my belief was that it was an insulation issue due to the extreme temperature variance, and pumping conditioned air there would be a constant struggle with the attic temperature extremes that encapsulate the room. I am open to considering a dedicated vent, although it seems like my utilities would likely jump as opposed to my thinking of insulation which would be a one-off cost.