Hi motown, I had a (possibly crazy) idea that I posted in a thread about another warm basement that might help you out.
Something to try, that will work at least in theory, to lower the temperature of something in a dry space is to build a really basic "swamp cooler" around a tree by wrapping it loosely with a natural wicking fabric or paper towels and then wetting the wrap down periodically; imagine wearing a wet t-shirt in front of a fan to increase the rate of evaporation and you will get the idea. The water carries heat away when it evaporates, leaving the interior of the wrap, or shirt, cooler. I would not do this for very long because the characteristics of the moistened branches will change and roots could begin to grow after a month or so, it could also cause fresh growth or buds to rot eventually and make your nipples hard and show through your shirt ;) A fan will really increase the cooling effect, but might dry out any trees in the area that are not wrapped and wet down regularly enough, especially recent transplants that have few roots taking up water.
It may just be crazy enough to work! I have much colder storage temperatures so have not had this type of problem and never dealt with it. Whatever you do, pick more than one good option so you will have more chances for success.
You could also probably put some back outside and cover them down to the ground against your house out of the direct sun. They will go dormant faster with near freezing temperatures and could be brought in for really cold nights and left in front of a drafty door to stay cool.
I read something else here a while ago about digging a pit to store figs outside, I think Herman2 did it but don't really remember the specifics. You could try something similar and bury one a foot or two deep in a well drained spot (sideways to prevent water from collecting in the pot) and mulch over top, then dig up in the spring.
edit: I meant no harm with the nipple joke, it seems a little less appropriate to me now, during daylight hours. Hope you are not offended.