Because it is a temperature dependence, we need to relate the capillary potential with surface energy, and this expression was given by Edlefsen and Anderson in 1943. They gave this expression experimentally, which related basically soil as a capillary potential to temperature.
Therefore if they are taken into account, this dependence into the velocity expressions we get a temperature term into the velocity as well, which is slightly different from the velocity expression which is in a isothermal flow.