Hydrogen storage in metal-doped carbons through a spillover mechanism has attracted a great attention. However, the data reported so far are lacking in consistency among different research groups, and the mechanism has not been fully revealed yet. In this work, we prepare a model Pt-loaded carbon by a simple and reproducible method in which already-synthesized Pt-nanocolloid is directly doped on zeolite-templated carbon. The Pt-loaded carbon thus obtained provides reliable data as for the temperature effects (273-353 K) on hydrogen/deuterium (H/D) adsorption isotherms, which contain the contributions of H2/D2 physisorption, H/D chemisorption on Pt surface, and H/D storage by the spillover mechanism. We extracted the last contribution (spillover H/D) from the isotherms, and found that the amount of the spillover H/D increases with increasing pressure (up to 100 kPa) and temperature (273-353 K). Detailed analysis of the number of H/D atoms stored by the spillover mechanism reveals that H/D radicals spilling from the Pt surface migrate on the carbon surface. The path integral molecular dynamics simulation also demonstrates the migration of atomic H/D on a model fragment of the zeolite-templated carbon, and suggests the enhancement of migration at higher temperature.