He is a jacksons, right? I have my two K. matschiei outside which are somewhat similar and mine are really freaking small. I have seen no issues with heat stress. Granted, I live up on the mountain and its always a few degrees cooler than in town and there is lots of shade. But, I think its better for them to take that heat being outside where there is a breeze and fresher air. The stagnant air inside is worse on them even if it is a little cooler. Ive had multiple montane species that I house outside in the warmer months around here (Hagerstown, MD area). They all were able to take warmer than usual temps as long as there was shade and plenty of cool mistings.
Here is what I would do. Take him outside where it is constantly shady if possible. Offer him a nice watering with the hose in the morning and one or two in the afternoon depending on how hot it is. If you are still in school or working see if someone can help you out with one or two of those waterings. Yes, the water will be cold but it will warm up if you use a misting setting on the water hose. (Whoever wants to bash me for this, bring it!). You do want it to be cool though because you are wanting to cool him down
If this is not possible a few other solutions come to mind. You can wet a towel with cold water, squeeze it out so its just damp and lay it over part of the cage. You may need to do this a few times throughout the day but if you cant do the latter this can keep the enclosure cooled down some. Another thing might be getting one of those big Gatoraid bottles or a 2 liter and freezing it then sticking it in the enclosure. If he feels its cooler in that area he may go near it. Id watch out for him wanting to rest on it though.
Its supposed to start cooling down a bit here come Thursday but as you know our summers can have some really hot spells.
Hope this helps.