Recirculating fluid heating systems

A liquid heating system includes an instantaneous heater (18) having an inlet (20) connected to a reservoir (62). The outlet (22) of the heater is connected to fixtures (72) which use the heated liquid, and is also connected through a return connection (30) to the reservoir. In an idle mode, a pump (40) draws liquid from the reservoir (62), so that the liquid circulates through the heater and back to the reservoir. A controller (52) actuates the heater to heat the liquid to a first setpoint temperature, so that the liquid in the reservoir stabilizes at the first setpoint temperature. In a supply mode, some or all of the heated liquid flows from the outlet to the fixtures (72). Cold liquid is admitted from a supply (60) to the reservoir, and cold liquid desirably also is supplied to the heater inlet along with liquid from the reservoir, so that the heater inlet receives a combination of these. The controller controls the proportion of cold liquid to liquid from the reservoir in the combination, so as to maintain the heater at a setpoint heating rate while also maintaining the temperature of liquid discharged from the heater outlet at or near a setpoint temperature.