Modelling fluid flow and heat transfer inside a mini-or micro-channel constitutes a challenge because it requires taking into account many effects that do not occur in traditional macrostructured systems. In a mini-channel, presence of solid walls, whose volume fraction is not negligible, modifies heat diffusion (conjugated heat transfer): this means that traditional Nusselt correlations for forced convection have to be revisited, because the heat flux distribution at the wall is not always normal to it and the location of the heat source modifies the distribution of the heat transfer coefficient in the flow direction. Our objective is to characterize the mean velocity U and the heat transfer coefficient of external exchange h and to describe the bulk temperature distribution T b (x). The inverse method makes it possible to go back to this information starting from measurement of the temperature fields on the two external faces of the channel and a corresponding model through the minimization of a criterion. In this work, the temperature fields can be obtained either by a numerical model or by an experimental model by infrared thermography. Before an experimental validation by infrared thermography, we perform numerical simulations and a sensitivity analysis of the external temperature fields to the mean flow velocity U and to the external heat transfer coefficient h. The temperature and flux distributions over the internal faces of the walls are estimated by an inverse method then.