Extending previous investigations on the cooling effect, the temperature distribution along a thermally isolated capillary through which He II is forced to flow after having passed through a superleak is measured. The temperature gradient at the entrance of the capillary is found to be numerically compatible with the earlier suggestion that heat conduction imposes a limit for cooling. The present results for low velocities appear not to be in agreement with the Gorter-Mellink model. At high velocities the temperature distribution becomes independent of the bath temperature nearly along the entire length of the capillary. From thermodynamics it is shown that the energy dissipated in the capillary is carried away by convective heat transport only, the velocity of the normal component at the end of the capillary being equal to the total mass flow velocity v.