In this paper, we propose a technique to select an appropriate convergence criterion for developing precise thermal compact model. It is known that the compact modeling in thermal simulation can reduce the computing cost for a system level of thermal simulation. We have used the Response Surface Methodology (RSM) to identify parameters of the compact model. However the resulting RSM model is not accurate enough, because the fitness function in thermal simulation has many peak points. We find that this is due to the insufficient convergence of thermal simulation, by investigating temperature results in thermal simulation with the change in thermal conductivities. To solve this problem caused by the insufficient convergence, we optimize the convergence criteria of temperature.