Moving with my bearded dragon

Hello!
Me and my boyfriend will be moving in March. And our bearded dragon will be coming with us to our new apartment. How do I make this less stressful for him? Also, late March might still be cold out since we live in Illinois. How should I travel with him in my car for a 20 minute drive? And what should I do at the apartment to make it easier for him to adapt?

Move him and his stuff in the same time period. I've used a large cooler for winter travel. Heat pack wrapped in a towel. Lid on. The air can be so cold I don't want my dragon to breath it at all, MN here. The cooler is large so I am not worried for short trips, your 20 minutes, your dragon will have enough air to breath. You can open the lid once you arrive. Set up the enclosure again. Then place him in the enclosure and give him a week of minimal attention so he can adjust to the new views, smells, and everything in the new place.

I've found that if you warm up the car to normal temps (comfortable for you, low 70s maybe) they do just fine. I regularly (pre-pandemic) made trips up to St Paul from Iowa even in the winter and ran into no issues. Having a heat pack on hand is good for long trips during the winter in case you need to stop. It won't be necessary for a 20 minute drive, especially in March. A cooler would work, so would a large box with some towels in it. I like using a pet carrier that straps into the seatbelt, but that may be overkill for a short trip.

Once you get to the new place, just set the enclosure up the same way you have it now. Let him get used to it again. If he seems to want to explore the new place a bit, I'd let him if it's safe to do so. They generally handle travel pretty well and I don't think it will be a problem for him.