Experimental temperature distributions on the external walls of a heated flat microchannel contain information on the temperature and velocity fields in the cross-section of the dynamically developed internal flow. The relationship between the heat source surface distribution on the external wall and the temperature field on the same or opposite face is derived using Fourier transforms of the temperature distribution in the direction of the water flow. The corresponding transfer function depends analytically on the velocity distribution. A sensitivity analysis of the temperature distribution to the velocity profile is implemented for different Peclet numbers in order to design a corresponding bench.