Using a cluster-flipping Monte Carlo algorithm combined with a generalization of the histogram reweighting scheme of Ferrenberg and Swendsen, we have studied the equilibrium properties of the thermal random-field Ising model on a cubic lattice in three dimensions. We have equilibrated systems of L x L x L spins, with values of L up to 32, and for these systems the cluster-flipping method appears to a large extent to overcome the slow equilibration seen in single-spin-flip methods. From the results of our simulations we have extracted values for the critical exponents and the critical temperature and randomnessof the model by finite size scaling. For the exponents we find v=1.02 +- 0.06, B=0.06 +- 0.07, y=1.9 +- 0.2, and mean(y)=2.9 +- 0.2.