We investigate the electrical and thermal transport properties of a sesquicarbide superconductor $La_2C_3$, including electrical resistivity, thermoelectric power, and thermal conductivity. The electrical resistivity exhibits a typical metallic character with a saturation behavior at high temperatures. The thermoelectric power shows a metallic behavior with pronounced phonon-drag effect, comparable with pure metals. The broad peak of the thermal conductivity is observed in the superconducting state, which is rapidly suppressed by magnetic fields. These observations suggest that the electron-phonon scattering is significant in $La_2C_3$, which is relevant with the relatively high-$T_c$ in $La_2C_3$ through strong electron-phonon coupling with low frequency phonon modes.