Assessment of the thermal characteristics of materials in heat exchangers with longitudinal fins is performed in the case where a conventional homogeneous material of a longitudinal fin is replaced by a functionally graded one, in which the fin material properties, such as the conductivity, are assumed to be graded as linear and power-law functions along the normal axis from the fin base to the fin tip. The resulting equations are calculated under two (Dirichlet and Neumann) boundary conditions. The equations are solved by an approximate analytical method with the use of the mean value theorem. The results show that the inhomogeneity index of a functionally graded material plays an important role for the thermal energy characteristics in such heat exchangers. In addition, it is observed that the use of such a material in longitudinal fins enhances the rate of heat transfer between the fin surface and surrounding fluid. Hopefully, the results obtained in the study will arouse interest of designers in heat exchange industry.