Try using a Rubbermaid with holes drilled in the lid for a soaking container instead of your bathtub. FAR less likely for a snake to crawl out. Fill with warm water (warm to the touch, no need to break out the thermometer) high enough so the snake can soak without having to swim in order to keep afloat.
I've NEVER been very precise when soaking snakes, definitely not to the point of using a thermometer, and I've owned 8 Burms (get respiratory infections if you look at them the wrong way) for over a decade. Always had great success with my Burms, never developed resp. issues.