I don't know if my story can help or not on moving with your kitty! I moved 2,700 miles with my cat, Rotten, back in September. More than a year prior to that, we moved 350 miles in April.
I know the advice is to make sure the cat is in a crate, but...I've never followed that rule. Thankfully I've had no escapees,either, but I feel awful cooping them up in a scary box when they're already nervous. I like them to be able to make themselves comfortable. I made sure she wore a collar, and when we had to leave the car I kept her on a leash. I kept a litter box in the car, but the one time she pooped, she pooped in my potted ginko tree. On the first move she got very carsick and pooped/puked on me...so I recommend keeping baby wipes and cleaning materials close by. I also like my kitty to have access to me for comfort. She spent a lot of the voyage in my lap or in her chosen safety zone--beneath a potted fern. She did come to enjoy it after a while, and loved watching cars.
For the heat, all I could do was keep the air conditioner going. I could see her panting if she was hot, and kept the air as high as necessary to prevent panting. I kept her foodbowl and waterbowl in the cupholders; she knew where they were, but never chose to use them. As to litterboxes anywhere...most cats I've known take VERY naturally to using litterboxes, but I've seen here that's no guarantee
There are cat-soothing materials,supposedly, sprays you can use to spritz on cars & houses in potentially stressful situations. I found some at a pet boutique and at Wal-Mart; vets may also carry them.
When we've arrived at new places, I certainly stayed home as much as possible to let her know I hadn't abandoned her. I kept her favorite basket & bed with us. Thank God, Rotten loves new places and new things. I was much more scared than she was about the first ventures outside. Here she's indoor, although she hates it. There she was indoor/outdoor. I could only take her crying for three days before letting her outside. We went outside on one short supervised trip, then I panicked and grabbed her back inside. The next day I stayed on the porch while I let her get as far away from me as she was comfortable with (which was less than fifteen feet). You've known Lancelot a lot longer than I knew Rotten when we moved; we'd only been together six months when we moved 350, and two years when we moved 2700 miles. If you feel comfortable with him, that's a lot of power to you.
Feel free to write me if there's anything I can help you on...don't know if this helped, but I've been there!