Implantable tube, for heating by conduction a heat transfer fluid for injection into all or part of a human or animal tissue, is provided with a wall having distal, median and proximal parts and comprising connecting elements for direct or indirect connection of the distal part to a fluid reservoir, and two means for connection to the terminals of an electric power supply, for incoming and outgoing current in the wall. The tube has a resistance less than 0.01.OMEGA. in its median and proximal parts, and a resistance of between 0.2 and 2.OMEGA. in its distal part. The median and proximal parts are connected electrically in series to the distal part; the tube having no additional electrical resistance.