While the CDT goes through Yellowstone, it’s not really the “highlight of the park” or anything… It just simply “passes through” on the most efficient trails that already happened to be there… i.e. heading through the southern part of the park. If you’re just looking for a good day-hike in Yellowstone, I wouldn’t limit yourself to the CDT.
If one of the main criteria of that day-hike is that it’s on the CDT… then, I think the best would be heading south from West Yellowstone toward Lone Star Geyser, and possibly as far south as the Shoshone Geyser Basin (not sure of the mileage off-hand). Another option would be Heart Lake… which does have a few hot springs, but isn’t really spectacular or anything.
Jonathan