In the present study we examine physical characteristics of a thin and rigid magnetic flux tube with a steady flow inside, which is embedded vertically upward in the solar atmosphere. We found from this study that (1) The downward material flow gives rise to a dominant heating in the flux tube which works with the conductive heating in the same direction. However, the upflow flow creates a dominant cooling which works against the conductive heating, resulting in a steeper temperature gradient with a shallower transition region. (2) Since the thickness of the transition region determines the material content in the transition region, a broader transition region of the downflow tube produces a larger differential measure.