Fouling is a common issue that requires careful monitoring and identification to ensure optimal heat exchanger performance. Typically, monitoring methods focus on controlled variables such as pressure, temperature, and the flow rates of hot and cold fluids. However, while some heat exchangers benefit from extensive historical data and a wealth of operational knowledge, others suffer from incomplete or insufficient information. This paper proposes a methodology combining Bayesian calibration to identify a data-driven model with transfer learning techniques. Utilizing temperature data from a well-documented source heat exchanger, we develop a reduced-order model through Bayesian calibration, applying a likelihood-free approach known as Approximate Bayesian Computation (ABC). After calibrating the source heat exchanger model, we can implement classifiers and conduct diagnostics by observing how the global heat transfer coefficient evolves as fouling impacts system performance. The expertise gained from the source heat exchanger can then be transferred to a target heat exchanger, which may differ in geometry or operating conditions but lacks the data required to calibrate a new model or train a new classifier. Our results demonstrate in which contexts and scenarios the classified and trained model from the source exchanger can be effectively reused for the target exchanger.