[en] Band-structure contributions to the specific heat of a low-density mobile gas adsorbed on a structured substrate are calculated directly with a perturbation expansion to second order in powers of the lateral Fourier components of the adatom-substrate potential. The formalism is applied to the case of helium adsorbed on basal plane graphite, with results in good agreement with those from a detailed band-structure calculation of Carlos and Cole. The perturbation expansion makes a substantial simplification in the specific-heat calculation. Qualitative features of the results are also discussed