We study numerical methods for coupled radiative transfer and electron energy equations. In highly opaque materials, strong coupling between them results in stiff source terms, making design of efficient and stable algorithms a challenging task. In this paper, we develop an efficient algorithm for multi-group radiative transfer equations coupled with electron energy equations. It is an integration method based on an ansatz of electron temperature. It poses no constraint on time step, and gives physically relevent solutions under reasonable assumptions. Numerical results show that the method is highly efficient and accurate.