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New considerations about the acceleration of an iterative process to couple the radiation transport equation and the equation of matter temperature are presented in this paper. Two synthetic acceleration methods [diffusion synthetic acceleration (DSA) and transport synthetic acceleration (TSA)] have been studied and analyzed, showing its strengths and weaknesses. This study is applied to an adaptive mesh refinement (AMR) context, concluding in a better performance of DSA for coarse level resolutions with higher Sn, while TSA is better for finer level boxes and smaller Sn cases. These conclusions are applied to accelerate the resolution of an AMR problem.