A transient-thermal model based on a lumped system is newly developed and implemented in a one-dimensional (1D), two-phase rigorous direct methanol fuel cell (DMFC) model presented in Part I. In this model, the main focus lies on the investigation of the transient thermal behavior of DMFCs and its influence on methanol crossover, cell performance, and efficiency. 1D simulations are carried out and the time-dependent thermal behaviors of DMFCs are analyzed for various methanol-feed concentrations and external heat-transfer conditions. Predicting the close interactions between the evolution of the transient temperature, methanol crossover, cell voltage, and efficiency during DMFC operations, the simulations of transient behavior indicate that the insufficient cooling of DMFCs finally lead to thermal runaway, particularly under high methanol-feed concentrations. Therefore, it is concluded that an efficient cooling system is greatly needed to safeguard DMFC operations and enhance the performance of DMFCs. The present 1D DMFC model is a useful tool for attaining a better understanding of complicated physical phenomena in DMFCs, which assists in optimizing the operating conditions of such cells and material/design parameters. (C) 2010 Elsevier Ltd. All rights reserved.