The application of large-eddy simulations to conjugate heat transfer problems can promisingly provide accurate results, including fluctuating heat loads which are critical for thermal fatigue. Such simulations rely on separate solvers and a coupling methodology which must be accurate and robust. In this context, the Hybrid-Cell Neumann-Dirichlet (HCND) coupling approach can adapt dynamically the coupling frequency given a desired accuracy. However, in order to determine statistics (mean, RMS,. . .) in a permanent regime, this approach must benefit from an acceleration technique which is here first derived and validated. Two configurations of a wall-impinging flame are then simulated: a quasi-steady case and a pulsated case. The former enables to validate the ability of the accelerated HCND method to predict a steady state wall temperature, while the latter highlights the retained acceleration which does not alter the fluctuations in wall temperature and wall heat flux. Both cases benefit from the self-adaptation of the coupling period provided by the method.