First, that super high water temp from summer, that's not good. What I did was get like 6 small, hard ice packs. I have string wrapped around their top and I float them in a big gallon freezer bag, that way they don't risk leaking, and the string prevents them from wandering about the surface. For emergencies, I use a few frozen water bottles. I mount them the same way because when they liquify, they can sink and pin down axolotls. The string prevents them from doing so but they seem to cool the tank pretty quick. Never hurts to just have those around. My axolotl dealt with like 66-70 degree water temp most of the summer because of the heatwave. I too, do not have air conditioning so I know how hard it is. Axolotls prefer like 55-65 degree water.
Second, do you test your axolotl's water parameters? I deeply recommend you get an API brand Freshwater Master Kit (got mine of Amazon for 30 bucks I think). Axolotls need low ammonia, like 0, low nitrites, and nitrates between 20 and 60, I think. There's a scale on the back of the directions on how to read them. It's hard to get the tank cycled properly because of it just taking a ton of time. If there's too much ammonia, your axolotl will get skin burns kinda, chemical ones, if there's too many nitrites, they were become very lethargic. I just had to deal with my axolotl's tank cycle. I reset it to deal with another issue and there were 2 weeks there I was doing a 5 gallon water change every other day, to keep her nitrites down. It makes them REALLY lethargic, like, when I pulled her out to tub her while I cleaned, she didn't fight me but the second she got into cool, clean water, she came back to life and was very pleased. High nitrates, I forget what they do, I think they deprive the water of oxygen or something. I am a major novice with this, I only know what I've written down from what others have told me.
Third, post some pics of your little guy! I wanna seeeeee. What size tank do you have and what kind of bottom? I have some ultra fine sand. I hope you know to not have any gravel in there since axolotls will eventually suck in some of the gravel when they go to feed. I'm just very curious and want to know how things are, from one new axolotl owner to another.