In the present paper, an optimal two-relaxation-time (OTRT) thermal lattice Boltzmann equation (TLBE) is proposed to simulate conjugate heat transfer. The derivation process is based on a developed idea of virtual heat capacity correction method. Finally, it is found that a unified TLBE can be achieved. The derivation process shows how the modified equilibrium distribution function works in simulating conjugate heat transfer. It also reveals the relation between the virtual heat capacity correction method and the method of reconstructing the equilibrium distribution function. By using Chapman-Enskog expansion, the proposed OTRT TLBE can recover the standard energy equation up to second-order accuracy. For validation, six test cases including both steady and transient conjugate heat transfer with flat or curved interfaces are calculated. The results show that the OTRT TLBE performs well in simulating conjugate heat transfer problems with both flat and curved interfaces, at both transient and steady states, and the OTRT TLBE could have better numerical accuracy than the single-relaxation-time (SRT) TLBE. (C) 2018 Elsevier Ltd. All rights reserved.