The excitation mechanism of the H(2) rotational temperature has been studied in a hollow-cathode glow discharge apparatus based on the measurements of relation between the rotational and cathode surface temperature. The rotational temperature evaluated by an excitation-emission model for the Fulcher-alpha transition indicates clear correlation with the surface temperature. Depending on the plasma parameters and neutral gas pressures, slight difference between both the temperatures is also observed. The temporal evolution of the rotational population densities predicted by rate equations suggests that the difference is attributable to an inequilibrium between the translational and surface temperature. Further possibility of an inequilibrium among the rotational, translational, and surface temperature is expected in low pressure or high electron density conditions.