In this paper an experiment design of the flash method dedicated to orthotropic material thermal characterization is considered. The present study relies on a comparative evaluation of the laser excitation duration time and intensity level, with respect to the measurement face, and their effects on the estimation accuracy of orthotropic material thermal diffusivities. The present estimation method, based on the well-known flash method concept, allows the simultaneous estimation of the three main thermal diffusivities. The identification method relies on the resolution of an inverse problem by means of a stochastic optimization algorithm retrieving the thermal properties by minimization of the least-squares criterion between the outputs of an analytical model and numerical predictions or experimental measurements. Both the direct analytical model and the estimation strategy are validated using an experimental test bench conducted on a carbon fiber reinforced polymer composite sample. The evaluation of various experiment designs, corresponding to different combinations of laser spot intensity and duration time, is conducted according to the face of the observation. A sensitivity analysis is conducted to complete the search of the optimal configuration. The present numerical study has enabled us to identify the rear face to be the most effective in order to successfully estimate the thermal diffusivities of such materials, especially the in-depth thermal diffusivity. For this configuration, excitation with a relatively long duration time (about 10 s in the present relatively low-diffusivity-material case), has been proved to be more convenient for such identification problems, compared to the impulse or very short pulse types.