Soaking is a great idea if done carefully. There are several places in YNP where it is allowed, officially or semi-officially.
In fact, every time I visit Yellowstone NP (like 5 times a year) it strikes me how silly it is that people are kept and are happy to stay on boardwalks and paved roads. They might just as well watch the BBC documentary and save everyone the trouble. If you are outdoors you should hike, swim, wade and sense the warm thermal waters. YNP is the most regulated and civilized park I know. I think this is sad.
Driving to Yellowstone on an interstate is probably more dangerous anyway.