The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random field and external field strength. Thermal states and thermodynamic properties are obtained for all temperatures using the Wang-Landau algorithm. The specific heat and susceptibility typically display sharp peaks in the critical region for large systems and strong disorder. These sharp peaks result from large domains flipping. For a given realization of disorder, ground states and thermal states near the critical line are found to be strongly correlated—a concrete manifestation of the zero temperature fixed point scenario.