Interleaving fins can significantly increase heat transfer by increasing the effective area per unit base area. The fins are separated uniformly by a gap, which is filled with a flow medium to control the heat flux. The heat flux between the plates depends strongly on the thermal conductivity of the fin material and the medium between them, as well as the dimensions. In earlier studies, an empirical fitting method has been used to determine the total effectiveness of the fins. However, it required complete characterization of the fins for each new set of operating conditions. In this paper, a simplified analytical model is developed, which still preserves the main physical traits of the problem. This model reveals the dimensionless parameter group containing both the material properties and the fin geometry that govern the heat transfer. Rigorous testing of the model using a numerical finite-element model shows an accuracy within 2% over a large parameter space, varying both dimensions and material properties. Lastly, this model is put to the test with previously measured experimental data and good agreement is obtained.