In this work, two industrial heating/cooling circuits are compared. One of the two systems failed in a short time showing severe corrosion damage and a through thickness crack close to one of the welds. The main difference between the circuits is the presence of a sodium molybdate-based corrosion inhibitor in the damaged one. The addition of these substances is very frequent in such applications, and they generally work very well in preventing serious corrosion attacks. Nevertheless, the technical literature reports other cases in which systems working with fluids containing such inhibitors failed prematurely. The authors performed a failure analysis of the damaged circuit focusing their attention on the regions where fluid leaks were observed because of through thickness cracks. This damage was located close to the pipe–flange weld. These zones were investigated by visual examination, radiographic and scanning electron microscope (SEM) analyses, metallographic observations by light optical microscope (LOM), Vickers micro-hardness tests and optical emission spectroscopy (OES) chemical analysis. The failure was related to the presence of severe pitting and crevice corrosion in the welded areas with the final activation of a further critical corrosion mechanism, i.e., stress corrosion cracking (SCC). In order to explain the shorter working life of the failed system, a physical model of the corrosion mechanisms acting on the two circuits was proposed.