Thermal transport properties at the metal/MoS2 interfaces are analyzed by using an atomistic phonon transport model based on the Landauer formalism and first-principles calculations. The considered structures include chemisorbed Sc(0001)/MoS2 and Ru(0001)/MoS2, physisorbed Au(111)/MoS2, as well as Pd(111)/MoS2 with intermediate characteristics. Calculated results illustrate a distinctive dependence of thermal transfer on the details of interfacial microstructures. More specifically, the chemisorbed case with a stronger bonding exhibits a generally smaller interfacial thermal resistance than the physisorbed. Comparison between metal/MoS2 and metal/graphene systems suggests that metal/MoS2 is significantly more resistive. Further examination of lattice dynamics identifies the presence of multiple distinct atomic planes and bonding patterns at the interface as the key origin of the observed large thermal resistance.