Numerical simulation of single bubble pool boiling process including transient thermal response of solid wall is performed using the ghost fluid method and the level set method for the sharp interface representation. The results show that non-physical initial condition in the numerical simulation deeply affects the process of bubble growth, and then multi-cycle simulation is necessary to eliminate its influence. It is shown by the present results that two nucleate criteria, i.e. constant waiting time and constant nucleate superheat, for determining the appearance time for the subsequent bubble lead to the same quasi-steady process of bubble growth if they are matched with each other. A periodically expanding and receding thermal ＂hollow＂ can be observed inside solid wall underneath the growing bubble. The recovery of the temperature on the nucleate site and the thermal boundary layer near the heating surface is influenced by transient heat conduction inside solid wall, which can affect evidently bubble thermal dynamics and heat transfer.