It would be possible for the lack of air conditioning to lead to heat exhaustion and mild dehydration, but typically that takes quite a while to cause constipation. However, cats don't always respond to things in a typical manner, so it's quite possible your theory is correct. I am still concerned about her tail, because of the swelling at the base of it, but that could be incidental. Tail movement is good, as long as she has full range of motion. In fractures, the tails are usually completely limp and very painful. In sprains the tail can have some range of motion but can still be so uncomfortable that urination and defecation is not possible.
I want to be clear in stating that there are very few things you can manage at home, and constipation is not one of them. If she is constipated, you may also see a distended or uncomfortable abdomen, lip smacking, drooling, gagging or vomiting, and a decreased to non existent appetite.
Make sure she has access to plenty of fresh water, and offer her canned food if you don't already (canned food has a very high water content, often tastes good and can be a sneaky way to help rehydrate her). You can even try some tuna in spring water, and just don't squish out all of the water. Monitor her litter box habits closely. If she stops eating, vomits, goes into the box and strains to either urinate or defecate, seems painful or just isn't acting herself, take her in right away. As long as she is eating, drinking and urinating and seems comfortable, you may be able to wait until Monday to have her seen.
Hopefully she became mildly dehydrated from the lack of AC and is just requiring a few days to get back to normal. Good luck with your baby.