In this paper, the axioms and procedures to define a thermoeconomic diagnosis theory, based on thermo-characterization, are presented herein. This theory can be applied for advanced energy systems. The thermo-characterization set for each component in a system a reference operating conditions in a three dimensional map (w, s, FR), and pre-evaluate all the effects when environmental variation, internal or control malfunction occurs (dw/dmalf, dw/dmalf). It should allow real-time monitoring in actual operating process, by determining matrix of malfunctions and its global thermoeconomic assessment. Results are validated with respect to an analytical simulator obtaining high accuracy.