Cross-flow three-fluid plate-fin heat exchanger is analyzed under both steady-state and transient conditions with a nonuniform inlet temperature of all the three fluids. The influence of the longitudinal heat conduction and axial dispersion in the separating sheets and three fluids, respectively, is also considered. Five different combinations (modes) of temperature nonuniformity in the three fluids have been considered and compared for the performance. An important phenomenon of temperature cross between/among the fluids has been observed and presented for certain modes of temperature nonuniformity and operating conditions. The effect in the performance has been presented on the basis of mean exit temperature and deterioration factor. Implicit finite difference technique has been used for the numerical solution. The heat exchanger's performance is found to be dependent on the mode of temperature nonuniformity, number of transfer units, and the operating parameters.