I'm back, and here's a link to a website I like. The article in this link talks about heat stroke, and also has numerous links to similar health issues related to heat, and in the green box to the right of the main discussion, there's more stuff about heat rash and abdominal cramps:
http://www.medicinenet.com/heat_stroke/article.htm
I think probably most of your health issues have to do with the Arizona heat. The rash and your higher body temperature, that's probably from the heat. Use mild soaps with laundry & bathing and rinse well, generally wear clothes that are 100 percent cotton, and use a little baby powder at the neck, to minimize chaffing. A lot of Southwesterners wear a bandana to soak up neck heat and wipe off their brow. But heat alone will sometimes cause a rash. So, sorry, but drinking more water will be what best minimizes the effects of heat.
The way to drink extra water to replace what you sweat out is by drinking a glass of water every time you are in the bathroom, make it a habit. I always guzzle at least a whole glass after I brush my teeth, I keep my own glass in there. Also, to get your water back and to keep cool, drink lots of ICED water, it tastes better cold and when you're hot and thirsty. By the way, sometimes lemonade and juices can further dry out a person...you can drink it, just not exclusively. I have a friend who hated water, but finally when health issues got out of hand, she started drinking it, and she feels better as a result.
The allergy thing may have to do with air conditioning, my husband cannot tolerate A/C because he gets stuffed up. So, I run the A/C for me and he sits at an open window, so we're both happy, and our bills are not particularly higher. I might add that even your digestive issues could very well be related totally to the heat, people get indgestion from overheating, ESPECIALLY when they don't replace water they sweat out.
One thing that might improve your digestion, too, is ordinary store brand 100 percent whole wheat bread, I eat it every day without fail, because I have digestive issues. Try different kinds, until you hit on one that seems to help your digestion. See, you gotta have enough bulk and quantity of food to have good digestion, and whole grains can do that better than almost anything. Also, dark green salads and fruit as a snack, especially blueberries, will cool you off and give you more bulk, keep the ingredients refrigerated.
Look up stuff online about heat stroke and the symptoms, see if any match up, especially the rash and digestive problems you're having. Also, there is a dermatology department at this website, just go to the list of forums (it's at the icon "forums" at the very top of this page) and post about your rash over there. Could be you'll find out your rash is from something entirely different than heat, so that's a good idea to post there.