  In this paper the three dimensional random field Ising model is studied at
both zero temperature and positive temperature. Critical exponents are
extracted at zero temperature by finite size scaling analysis of large
discontinuities in the bond energy. The heat capacity exponent $\alpha$ is
found to be near zero. The ground states are determined for a range of external
field and disorder strength near the zero temperature critical point and the
scaling of ground state tilings of the field-disorder plane is discussed. At
positive temperature the specific heat and the susceptibility are obtained
using the Wang-Landau algorithm. It is found that sharp peaks are present in
these physical quantities for some realizations of systems sized $16^3$ and
larger. These sharp peaks result from flipping large domains and correspond to
large discontinuities in ground state bond energies. Finally, zero temperature
and positive temperature spin configurations near the critical line are found
to be highly correlated suggesting a strong version of the zero temperature
fixed point hypothesis.
