We show that the lattice contribution to the thermal conductivity of MoS2 strongly dominates the carrier contribution in a broad temperature range from 300 to 800 K. Since theoretical insight into the lattice contribution is largely missing, though it would be essential for materials design, we solve the Boltzmann transport equation for the phonons self-consistently in order to evaluate the phonon lifetimes. In addition, the length scale for transition between diffusive and ballistic transport is determined. The low out-of-plane thermal conductivity of bulk MoS2 (2.3 Wm-1K-1 at 300 K) is useful for thermoelectric applications. On the other hand, the thermal conductivity of monolayer MoS2 (131 Wm-1K-1 at 300 K) is comparable to that of Si. © Copyright EPLA, 2016.