I can sympathize with the heebee-jeebees from the creepy-crawlies and the "heat exhaustion". Moving here from Minnesota was definitely an adjustment for me, and you have to come to terms with the fact that you will see many more bugs, and big ones, in a month than you probably ever have in your life before. Mostly, I try to avoid thinking about bugs as much as possible - but I have gotten a lot less squeamish about them.
When we moved and became responsible for pest treatment, I got a spray that supposed is effective for a whole year and is pet-safe once dry. It seems to be very effective, as all I have found are dead bugs inside. That is my first line of defense. My second is a cat that hunts and kills every kind of insect or spider. In our last place, we had about an inch and a half gap under the front door. It was not uncommon to wake up to a cat-killed roach in the middle of the living room and/or kitchen and I had a flip-flop I used solely for killing bugs and spiders. Thankfully, the doors in our new place actually fit the frames and the weather stripping is intact!
Closing up what gaps you can and keeping the kitchen clean will help. If you don't already, rinse all dishes before leaving them for any length of time. Change the garbage frequently. Sweep at least once a day even if it doesn't look dirty, especially in the corners where spiders like to hide.
Get a fan for the heat. And drink a LOT of fluids. The heat is worse if you're dehydrated. Also be prepared to shower at least once, if not three or four times, a day and wash all your clothes after one wear. You will sweat more than you believed possible, especially before you're acclimated. Maybe make really good friends with someone who has AC and just hang out with them all summer.
Though we haven't had any in our new place yet!
