Adequacy of various definitions of polaron effective mass ${m}^{\mathrm{*}}$ is examined. The expression for ${m}^{\mathrm{*}}$ obtained by using the zero-temperature kernel is compared with the zero-temperature limit of the temperature-dependent effective mass obtained by employing the finite-temperature kernel. We find that consistent results are obtained when Saitoh's definition is employed. Our calculations are illustrated for a simple case of weak electron-phonon interaction.