Chernobyl used a neutron moderator with a positive temperature coefficient of reactivity (liquid sodium), while U.S. Navy reactors use water, which has a negative coefficient of reactivity. The more energy you put into the water surrounding the reactor, the less reactive it allows the reactor to be. This has a stabilizing effect on the system. U.S. Navy reactors are inherently stable and inherently safe. To answer your question directly, yes entropy will trend toward making the reactor produce less heat with no intervention.