I transport Tali in the cabin of my car (I keep it comfortable for me, so 75-80 degrees) when I transport her, and we keep on the floor near the heater and she's always been fine, not to cold and not to hot. If I have to run errands, I bring her in with me (usually in my purse) so she doesn't get cold or hot in the car.
I also put her in a little critter keeper like container- I had her in a pillow case, but my dog (while bouncing around) landed on it. The keeper has hard plastic sides so its sturdy and more like a hide- I feel like its a bit more secure for her. I need to get a bigger one because she's quickly out growing it.

(Her travel container which, again, is getting to small)

Tl:dr- your guys in plastic tubs that are belted in should be fine without added heat packs... just don't leave them alone in the car because it could quickly get very cold. If you need to stop in somewhere, I'd put them in pillow cases (and then put the pillow cases in the tubs while traveling) and take them in with you in a messanger bag.

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