An improved shell-and-tube steam instantaneous heat exchange system of a closely coupled feedback design which overheats water in the heat exchanger portion of the system and then blends the water, as needed, with proportional amounts of cold water to achieve the correct outlet temperature for a wide range of flow rates. The system uses at least two primary heat exchangers to provide redundancy in the case of failure of a major component of the system. Steam flow through the heat exchangers is controlled by the use of steam traps, rather than using a thermostatically controlled valve to vary the supply of steam. To obtain precise temperature control during varying water volume use, water is directed from the blended outlet of a first water tempering valve into the hot inlet port of a second water tempering valve. The first valve is designed to blend cold and hot water to a predetermined temperature which is higher than the second water tempering valve, so as to bias the second tempering valve, thereby minimizing thermal hunting and providing tighter temperature control from the second tempering valve.