[en] Thermal dispersion in a granular medium results from the combined effects of heat diffusion in both the fluid and solid phases and of thermal conduction in the fluid. These phenomena require some kind of averaging in order to be modelled at the mesoscopic scale. A model using a local mean 'enthalpic' temperature and a filtration velocity has been developed and its two dispersion coefficients have been experimentally estimated and presented under the form of correlations, for water or air flow. This model is valid far from the wall, but in the near-wall region, local heterogeneity should be taken into account. The purpose of this study is to detect the effects of such a heterogeneity, by the mean of an experimental parameter estimation validated by a Monte Carlo-type simulation. The results show that the thermocouple locations are biased at the end of this process. So a better model with at last two layers has to be designed in order to model the observed measurements. (authors)