A new model of the single-blow problem is proposed, considering the lateral heat conduction resistance along the fins. the axial heat conduction along the separating plates and the axial thermal dispersion in the fluid. For plate-fin heat exchangers made up of stainless steel, the effect of the lateral heat conduction resistance along the fins can usually not be neglected. This effect is taken into account by solving the temperature dynamics in the fluid, separating plates and fins simultaneously. The axial dispersion model is used to take flow maldistribution in plate-fin heat exchangers into account. The effect of the axial heat conduction in separating plates is also considered. The governing equation system is solved by means of Laplace transform and numerical inverse transform algorithms. The investigation confirms: for plate-fin heat exchangers of aluminium the effect of the lateral heat conduction resistance of fins can usually be neglected because of their high fin efficiency. However, the assumption of uniform porous medium is not valid if the plate-fin heat exchangers are made up of stainless steel. In such a case the heat conduction resistance of fins has significant influence on the outlet fluid temperature variation.