A tube of a thermal regulation device for cooling electrical energy storage members is disclosed. The tube extends in a longitudinal main direction of elongation. The tube includes a plurality of longitudinal channels for circulating heat transfer fluid that are formed one beside the other in the material inside the tube. The longitudinal channels open out onto each longitudinal end face of the tube. The longitudinal channels are divided into a first assembly for circulating heat transfer fluid and a second assembly for circulating heat transfer fluid. At least one longitudinal end face of the tube includes a sealing zone which is disposed between the channels contributing to forming the first circulating assembly and the channels contributing to forming the second circulation assembly.