The invention concerns a handpiece for injecting vapour into an animal or human vessel in order to heat said vessel, said handpiece comprising means for generating vapour from a liquid such as water or physiological liquid and a connection member (8) for connection to a catheter (2) or a needle to be inserted into the vessel in order to inject the steam into same. The means for generating vapour comprise a heating reservoir (6, 7) intended to contain the liquid, and is provided with electrical heating means, for heating the liquid in order to vaporise same and produce a flow of vapour diffusing continuously via the connection member (8).
