Heat exchangers have been widely used in various engineering fields. “No source”, “Downgrading” and “Steady state” are three main traits of traditional exchangers, because of which there exist some limitations in their applications and analysis. For an ordinary heat exchanger, the cold fluid outlet temperature can never exceed the hot fluid inlet temperature (Tc,o<Th,i), so that the effectiveness cannot exceed unity. Nevertheless, in practical engineering applications, cold fluid with much higher outlet temperature is sometimes needed, even hope it higher than the hot fluid inlet temperature (Th,i). Hence the heat exchange effectiveness and the outlet temperatures are restricted for traditional exchangers. In this paper, starting from the former two features, by bring in thermal-work conversion equipments (heat engine and heat pump), the new concept of generalized heat exchanger is put forward to partly make up the deficiency of the traditional ones. Meanwhile two typical new heat exchange processes (“Two in, Two out” system and “Two in, Three out” system) are established. Through two case studies, the thermal performance of the new systems is analyzed. The results indicate that such generalized heat exchangers can break through the outlet temperature limitations and improve the effectiveness to some extent such that the distribution of “quantity” and “quality” of heat energy can be controlled during the heat transfer process. Thus the new concept may be of great significance for simplifying analysis and instructing practical engineering applications.