The software compensation algorithms developed for the CALICE Analog Hadron Calorimeter are extended to incorporate time information on the cell level, and the performance is studied in GEANT4 simulations with a detector model of a highly-granular SiPM-on-tile calorimeter. The addition of ns-level time resolution is found to result in significant improvement of the energy resolution for local software compensation, with further improvement possible with better resolution. The high correlation of energy density and time variables show that both provide sensitivity to correlated underlying shower features, which limits the potential of timing information when used as a global rather than a local variable.