A handpiece for injecting steam into a human or animal vessel in order to heat the vessel, including a steam generator for generating steam from a liquid and a connection member for connecting a catheter or a needle that is to inject the steam into the vessel. The steam generator includes a reservoir to contain the liquid, the reservoir being equipped with electrical heating means for heating the liquid in order to vaporize it and produce a stream of steam that diffuses via the connection member. The steam generator also includes a first nonreturn outlet valve interposed between the reservoir and the connection member for preventing fluid from passing from the connection member toward the reservoir. The first irst nonreturn outlet valve being a pressure-regulating valve which opens to allow steam to pass from the reservoir toward the connector when the pressure in the reservoir has reached a threshold value.
