Impossible to know, as I'm not seeing the size of your snake compared to the size of your smaller cooler. If it's too crowded, he might be more stressed & pushing
up the lid? For my smaller snakes (corn snake or rosy boa), I'd use a "lunch size" cooler to carry them...but don't forget you need space for the hot water bottle &
maybe some more padding too? Your call...
You could pre-warm the ice chest with a heating pad too, that will work also. If you're worried about air (in the smaller one) you could put a small piece of tape in the
opening so it just doesn't close so tightly.