  We have developed a set of four fully coupled Boltzmann equations to
precisely determine the relic density and temperature of dark matter by
including three distinct sectors: dark matter, light scalar, and standard model
sectors. The intricacies of heat transfer between DM and the SM sector through
a light scalar particle are explored, inspired by stringent experimental
constraints on the scalar-Higgs mixing angle and the DM-scalar coupling. Three
distinct sectors emerge prior to DM freeze-out, requiring fully coupled
Boltzmann equations to accurately compute relic density. Investigation of
forbidden, resonance, and secluded DM scenarios demonstrates significant
deviations between established methods and the novel approach with fully
coupled Boltzmann equations. Despite increased computational demands, this
emphasizes the need for improved precision in relic density calculations,
underlining the importance of incorporating these equations in comprehensive
analyses.
