Low voltage cabling - insulation
If there's no heat in this closet, and it has two external walls, and its only heat is whatever bleeds from the bedroom, then it will inevitably be colder than that bedroom. Frankly, a 2 degrees (F?) difference doesn't seem like a lot in this situation.

My reasoning? In cold weather, heat will flow from that closet through those two outside walls and into the great outdoors. The only way heat will enter the closet is through the  doors and wall shared with the bedroom, and that will only happen if there's a difference in temperature between the bedroom and the closet.

Insulation will help a bit, but either adding explicit vents between the closet and bedroom, or actually adding a heater to the closet, is the only way you'll significantly reduce that temperature drop.