I've used dog carriers in the past for my water dragons when I had them. Placed a towel on the bottom to collect feces and give them something to hold onto. I don't know if you'd be able to do this for the tegu, but it'd be something to consider for the beardies. I housed them individually for travel to minimize the potential for fights, but depending on your individuals and the size of the carrier you might be able to house them two a piece. I used something similar to this.
During travel, I usually aim to keep my animals around 75*, and not much lower or higher. Monitor them consistently and keep them out of direct sunlight if you can, since those windows tended to make my animals uncomfortably warm. Window shades for your car can help to eliminate this problem though.
I always pack hand warmers in case I can't keep them warm enough to be comfortable (which usually isn't an issue except in winter). Just get a few packs from Walmart, and, depending on the size of the animal, wrap a few in paper towel and place in the enclosure with them in case they need the heat in a pinch.
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