The main purpose of this paper is to implement some convenient analytical solutions of the two-dimensional convection–diffusion equations in a multilayered system, in the form of some relationships between average temperature fields, based on the thermal quadrupole formalism. Some equivalent analogical networks are proposed in order to implement the model in a more convenient form, based on the electrical analogy. The important advantage of such approach is to connect different layers through simple network connections between the respective interface variables. Special emphasis is laid on the case where the lateral boundary conditions correspond to insulated walls. The transient case is also presented, for non-insulated lateral boundary conditions, coupled with a third layer. Some examples are given in order to illustrate the suitability of the proposed model in the case of temperature field image processing in a microfluidic chip.