This paper systematically studied two transversely coupled qubits' heat transfer in contact with independent and common heat reservoirs. We reveal that common heat reservoirs can slightly suppress the steady-state heat currents compared to independent heat reservoirs, and the transverse coupling of qubits can enhance the suppression roles. In particular, in the case of resonant coupling of two qubits and the proper dissipations, the steady state can be decomposed into a stationary dark state which doesn't evolve and contributes zero heat current, and a steady state which corresponds to the maximal heat current. This dark state enables us to control steady-state heat current with an external control field and design a thermal modulator. In addition, we find that inverse heat currents could be present in the dissipative subchannels between the system and reservoirs, which interprets the suppression roles of common heat reservoirs. We also find that heat current for a given system has a similar changing tendency to the concurrence of assistance with temperature.