The energy density of a non-interacting massive Bose field in lattice thermodynamics is considered. The deviations from the continuum limit due to both the finite volume of the system and pure lattice effects are studied. A considerable increase in the lattice corrections in the region of small (as compared with the field mass) temperatures is detected. The role of the latter in the estimate of the glueball mass obtained from lattice gauge thermodynamic data is pointed out.