I haven't had any heat issues as of yet. I do have a filtered AC vent in the back of the closet, so that has helped. The vent has also been equipped with an easy-to-access damper so I can shut it off in the winter when the heat may be on. Despite all of this, I am going to investigate some fan solutions to better circulate/vent air within the closet.

It may be as simple as a vent on the backside blowing air from the closet into the unfinished attic space.