Finite temperature effects in the supergravity dual of the N=1 gauge theory

We consider the supergravity dual of the N = 1* theory at finite temperatur e by applying the Polchinski-Strassler construction to the black D3-brane s olution of type-IIB supergravity. At finite temperature the 5-brane probe a ction is minimized when the probe falls to the horizon, although metastable minima with t >> r(H) persist for a range of temperatures. Thermal effects on the 3-form source for the chiral multiplet mass m and its order m(2) ba ck reaction on the other fields of the IIB theory are computed. We find uni que solutions which are regular at the horizon and have the correct behavio r on the boundary. For fixed temperature T, the horizon shrinks for increas ing m(2) suggesting that there is a critical temperature separating the sys tem into high and low temperature phases. In the high temperature phase 5-b ranes are unnecessary since there are no naked singularities. Using the ord er m(2) correction to the horizon area we calculate the correction to the e ntropy to be Delta (S) = -0.1714N(2)m(2)T, which is less than the free fiel d result.