A heat transfer model on a microfluidic is resolved analytically. The model describes a fluid at rest between two parallel plates where each plate is maintained at a differentially specified temperature and the thermal conductivity of the microfluidic is spatially modulated. The heat transfer model in such micro-hydrostatic configuration is analytically resolved using the technique of the Laplace transform applying the Bromwich Integral and the Residue theorem. The temperature outline in the microfluidic is presented as an infinite series of Bessel functions. It is shown that the result for the thermal conductivity spatially modulated has as a particular case the solution when the thermal conductivity is spatially constant. All computations were performed using the computer algebra software Maple. It is claimed that the analytical obtained results are important for the design of nanoscale devices with applications in biotechnology. Furthermore, it is suggested some future research lines such as the study of the heat transfer model in a microfluidic resting between coaxial cylinders with radially modulated thermal conductivity in order to achieve future developments in this area.