It is a good idea to ease up on the heat in the shower, even though a hot shower feels great and is very relaxing. Too much hot water can be very drying and irritating. 

If you're using Dan's moisturizer, a few people have reported sensitivity to the licorice root extract which gives the moisturizer its color. If you're concerned that may be the problem, try subbing a different moisturizer and see if that helps.

Overall, people doing the Regimen experience dry, red, irritated skin for awhile until their skin adjusts to the treatment. So your skin may just be reacting to the whole thing, and the hot showers are probably not helping.

Hope this is helpful!

How has your skin been ?