Laminitis is commonly known as founder. It is the inflammation of the laminae the tissue that surrounds the coffin bone inside the hoof.
Because of the rigid hoof wall, it can not expand, so the swelling may or may not be visible at the coronary band. The affected hoof will feel warmer than the other feet that are not affected. You may have to check a front foot for comparison because the other hind foot may be warmer than normal as well because of him allowing the sore foot relief by not standing on it.
Cold hosing, icing, or standing the horse in a cool pond is part of the treatment for reducing the swelling. You may also put the horse on a pain killer temporarily to help him deal with the pain of walking on it. Consult a quality farrier or a vet preferably on how to treat it in the future and to try to prevent it.