So all you need is Heater
No.
To keep the stock healthy while in the holding tanks, during teardown and rebuild, which is going to take at LEAST several days, probably a week or more, you MUST have flow in order to break surface tension of the water or it will stagnate and everything will be lost.
For the actual move, meaning the time in the car from old to new, you don't need anything. They will be fine for that long.
I would set up your totes now, get the rocks and stock out of the tank asap, and into the totes. Then you can tear the tank down at a reasonable pace and not be pressured by doing it at the last minute.
The day of the move, put everything into 5g buckets, get it into the car and go. As soon as you get to the new place, get the totes set back up ASAP. Try and save as much water as you can since you won't have a supply on hand other than what you bring with you. everything out of the buckets and into the totes, flow makers and heaters on.