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We have developed a fast, low power heat switch for switching a niobium thin film between the normal and superconducting state. The sputtered niobium film (400 nm thick, 100 μm wide) has a critical current density of 5×1010 Am-2. Switching is produced by joule heating a small section of the niobium film with a titanium thin-film resistor. With the heat switch in vacuum, the minimum heater power needed to switch to the normal state was 4.5×10-5 W. A simple three-dimensional thermal model shows that the minimum power is primarily determined by the thermal conductivity of the substrate. We have achieved response times less than 10-6 s.