A finite element code is used to analyze the conjugate heat transfer over the external side of a single-row plate-fin and tube heat exchanger. The conditions for which the simulations are conducted are similar to those of real plate-fin and tube heat exchangers where both conduction through the fins and convection over them are present. The influence of several parameters on the temperature distribution and local heat transfer is analyzed. From the simulations it is seen that the region of high heat transfer that appears in the leading edge of the fins is the most affected by the finite conductivity of the fin material. There is a decrease of the local heat transfer there when either the fin conductivity or the fin thickness is decreased. This is due to the decrease of the temperature gradient between the fin leading edge and the entering fluid. The effect of increasing the Reynolds number is to reduce the efficiency of the fins. This causes the local Nusselt number not to grow as fast as it would have grown if the fins had infinitely large conductivity. Finally, the effect of the eccentricity of the tube with respect to the fin length is studied. The results illustrate that by moving the tube nearer to the trailing edge of the fin, the area of low heat transfer behind the tube is reduced in size and, at the same time, the temperature gradient between the fin leading edge and the fluid above is reduced causing a reduction of the heat transfer ahead of the tube. This suggests that there is an optimum position of the tube with respect to the fin length.