Our initial reaction is to suggest that you ask your remodeling contractor how he intends to resolve the uncomfortable state that he left you in. In the event that he is not available, we have a solution for you.
Cut a small access hole in the closet wall and fill the wall cavity with batt-insulation. The recommended R-value for walls in attics is R-11, but we suggest R-30. R-30 doesn't cost much more than R-11, but the resultant insulative value is amazing. Use craft-backed insulation the kind with paper backing is best. Place the papered side toward the inside of the home. This will help reduce condensation at the interior side of the wall.
Also, it would be a good idea to consider leaving the hole to do the insulation work for future access to the attic. When cutting the access hole be careful to make perfectly horizontal cuts (a razor knife works great) at the center point of two adjacent wall studs. Perpendicular-horizontal cuts, making up the last two sides of the opening, can be backed with solid wood blocks and used in conjunction with the half-exposed wall studs to create a solid base to hold the previously removed wall board. If you are careful not to damage the piece of wallboard during removal you can use four screws to replace it saving the cost of purchasing new wall board.