We use cellular dynamical mean field theory with the continuous-time quantum Monte Carlo solver to study the Kane-Mele-Hubbard model supplemented with an additional third-neighbor hopping term. For weak interactions, the third-neighbor hopping term drives a topological phase transition between a topological insulator and a trivial insulator, consistent with previous fermion sign-free quantum Monte Carlo results [H.-Hung et al. Phys. Rev. B 89, 235104 (2014)]. At finite temperatures, the Dirac cones of the zero temperature topological phase boundary give rise to a metallic regime of finite width in the third-neighbor hopping. Furthermore, we extend the range of interactions into the strong coupling regime and find an easy-plane anti-ferromagnetic insulating state across a wide range of third-neighbor hopping at zero temperature. In contrast to the weak coupling regime, no topological phase transition occurs at strong coupling, and the ground state is a trivial anti-ferromagnetic insulating state. A comprehensive finite temperature phase diagram in the interaction-third-neighbor hopping plane is provided.