A critical review of current methods for monitoring the performance of heat exchangers in the presence of fouling highlights a number of pitfalls. An improved analysis method and visualization of operation data (the TH-lambda plot) are proposed, which enable to accurately and rapidly estimate the location and extent of fouling, the properties of the deposit, and their impact on exchanger performance. The method uses advanced dynamic thermo-hydraulic models to analyze the data. The visualization presents this information in a way easily interpreted by field engineers. The superior features are demonstrated on various applications, where traditional methods give poor visibility or outright wrong information about underlying events. These include organic fouling deposition and aging, incomplete cleaning, multicomponent deposits, and changes in fouling behavior. First, the basic concepts are illustrated with idealized examples (constant inlet conditions, using simulated data). The approach is then applied to three real refining case studies, with pressure drop either measured or generated via soft sensors. The results show that the advanced dynamic models used enable to properly integrate and interpret highly variable data measurements, explain complex underlying thermal and hydraulic effects, adequately monitor performance, and rapidly detect changes in fouling behavior. The approach provides a new practical tool for monitoring of heat exchanger performance and early fouling diagnosis.