The finite-temperature phase diagram of the Hubbard model in d = 3 is obtained from renormalization-group analysis. It exhibits, around half filling, an antiferromagnetic phase and, between 30%-40% electron or hole doping from half filling, a new tau phase in which the electron hopping strength t asymptotically becomes infinite under repeated rescalings. Next to the tau phase, a first-order phase boundary with very narrow phase separation (less than 2% jump in electron density) occurs. At temperatures above the tau phase, an incommensurate spin modulation phase is indicated. In d = 2, we find that the Hubbard model has no phase transition at finite temperature.