Flows and heat transfer through periodic structures have been extensively investigated for their importance in numerous industrial applications such as heat exchangers and heat sinks. When neglecting the fluid property changes along the flow passage, the flow field is identical in consecutive periodic units, and the temperature field also exhibits similar patterns. To simulate such systems efficiently, appropriate transforms and boundary conditions have been developed, such that only one periodic unit is needed to calculated while the simulation results can be readily applied to multiple units along the periodic passage. However, existing simulations are limited to two types of periodic thermal flows: constant temperature or specified surface heat flux over all surfaces. Such requirements on the surface thermal conditions in general are not valid or not available in practical systems. In this study, a novel numerical treatment is proposed for such periodic thermal flows. Here the physical temperature is decomposed into two parts: the transient part that decays along the flow, and the equilibrium part which remains the same over all units. The two temperature parts are solved separately under appropriate boundary conditions. This temperature decomposition method (TDM) has been tested in several demonstration systems with various thermal boundary conditions and also conjugate heat transfer situations. These carefully designed demonstration simulations show the validity, accuracy, and capability of our method. This work could be valuable for research and applications in heat transfer processes through periodic structures.