The cooling jackets of liquid rocket engines are composed of narrow passages surrounding the thrust chambers and ensure the reliable operation of the engine. Critical conditions may also be encountered, since the cooling jackets of cryogenic engines, such as those using LOX/LCH4 propellants, are based on a regenerative strategy, where the fuel is used as a refrigerant. Consequently, deterioration modes near where pseudocritical conditions are reached or low heat transfer coefficients where the fuel becomes a vapour and must therefore be managed. The verification of the cooling jacket behaviour to consolidate the design solutions in all the extreme points of the operating box represents a very important phase. The present paper discusses the full characterization of the HYPROB (HYdrocarbon PROpulsion test Bench Program) first unit of the final demonstrator, (DEMO-0A), by considering the working points within the limits of the operating box and comparisons with the nominal conditions are given. In this way, a full understanding of the cooling system behaviour, affecting the working of the entire thrust chamber, is accomplished. Moreover, the design strategy and choices have been confirmed, since the verifications also include potentially even more extreme conditions with respect to the nominal ones. The investigation has been numerically performed and supported the thermo-structural analyses accomplished before the final firing campaign, completed in December 2022. Since little information is available in the literature on LOX/LCH4 engines, suggestions are given as to the organization of the numerical simulations, which support the design of such rocket engine cooling systems.