B.B.
Does the rash have small white bumps on it? Feel the back of his arms and legs as well. My daughter has something called Keratosis Pilaris (KP). It took me forever to have it diagnosed properly - everyone kept saying it was eczema. KP is a genetic condition - many people have these bumps on the backs of their arms. It is not contageous or harmful. It can be aggravated by extreme heat or cold, especially on the face, and become red and the bumps more pronounced. It can sometimes be itchy (although, my daughter has not had this symptom), and it feels like she has dry, rough patches. It can become better with age, but at a young age, there is not much you can do about it except use some good moisturizing creams. When he gets older, you can use some prescription medications if it bothers him, but it's really not a big deal. Obviously, check with your dermatologist - that's who finally diagnosed my daughter, to see what it is for sure.
In the mean time, here's a link to the Mayo Clinic's information on it:
http://www.mayoclinic.com/health/keratosis-pilaris/DS00769