Hey, please forgive me for not responding sooner to your posts. Due to the severity of your situation, I would have responded back promptly, however we were hardly at home at all today. The way you are describing Kimber does worry me greatly, especially him going limp.
Please check out this link, to evaluate your rabbits symptoms to see if they match up. Lethargy is a sign of heat exhaustion! But please take a look at the other symptoms to see if any you have forgotten to mention just so happen to match up.
http://myhouserabbit.com/rabbit-health/recognizing-heat-stroke-in-your-pet-rabbit/
The suggestions given in the link are also some great solutions!!! So be sure to check them out.
I am not a veterinarian, but do have much advice to give from extensive research I have done in the past. I would recommend calling your rabbits’ vet, and explaining the symptoms they are experiencing and your current situation- and ask for advice as to whether or not they are experiencing heat stroke.
Do you know when you will be getting your AC fixed/replaced ?