This paper discusses the influence of thermal conduction along the cable on the propagation of normal zones in force-flow cooled conductors. It is shown that because of conduction in the cable, and because of a temperature gradient between the cable and the cooling helium, the normal zone always propagates faster than the speed of the helium being ejected from the normal zone: the normal front advances the heated helium slug. Expressions to estimate the front advance speed are given, and its influence on the global propagation speed is discussed.