A fluid heater apparatus has fluid discharge temperature control to prevent temperature overshoot. A plurality of heater elements are employed and at least certain of the heater elements are independently controllable. At least one of the heater elements is employed as a “finishing” heater element, with the other heating elements deactivated to enable the “finishing” heater element to more slowly elevate the temperature of the fluid in the body from a first temperature reached by activation all or most of the heater elements to the predetermined discharge temperature. One of more of the heater elements may have a different power output than the other heater elements.