A transient testing technique is developed to evaluate the thermal performance of industrial-scale heat exchangers. A Galerkin-based numerical method with a choice of spectral basis elements to account for spatial temperature variations in heat exchangers is developed to solve the transient heat exchanger model equations. Testing a heat exchanger in the transient state may be the only viable alternative where conventional steady-state testing procedures are impossible or infeasible. For example, this methodology is particularly suited to the determination of apparent fouling levels in component cooling water system heat exchangers in nuclear power plants. The head load on these so-called component coolers under steady-state conditions is too small to permit meaningful testing An adequate heat load develops immediately after a reactor shutdown when the exchanger inlet temperatures are highly time-dependent. The application of the analysis methodology is illustrated herein with reference to an in-situ transit testing carried out at a nuclear powerplant. The method, however, is applicable to any transient testing application.