This paper presents the results of research on heat transfer during fluid flow in a heat exchanger with two rectangular mini-channels. There was Fluorinert FC-72 flow, heated by the plate in the hot mini-channel, and co-current flow of distilled water in the cold mini-channel. Both fluids were separated by the copper plate. A thermal imaging camera was used to measure the temperature distribution of the outer surface of the heated plate. The purpose of the calculations was to determine the heat transfer coefficients at the contact surfaces: the heated plate—FC-72 and FC-72—the copper plate. Two mathematical models have been proposed to describe the heat flow. In the 1D approach, only the heat flow direction perpendicular to the fluid flow direction was assumed. In the 2D model, it was assumed that the temperature of the heated plate and FC-72 and the copper plate meet the appropriate energy equation, supplemented by the boundary conditions system. In this case, the Trefftz functions were used in numerical calculations. In the 1D model, the heat transfer coefficient at the interface between FC-72 and the copper plate was determined by theoretical correlations. The analysis of the results showed that the values and distributions of the heat transfer coefficient determined using both models were similar.