Two numerical methods, one for axisymmetric compression and the other for axisymmetric torsion, have been developed to predict nonsteady-state temperature fields in these deformation processes. In compression, the upper-bound method has been used to determine the velocity field prior to temperature calculations. In both compression and torsion, the predicted temperatures agree well with experimental data obtained by other workers. The compression analysis has been also used for investigating (1) the effect of friction upon temperatures and (2) the effect of ram speed upon metal flow and temperatures. The results of these investigations indicate that the numerical approach predicts, within approximations, the trends observed in experimental studies.