In divertor tokamaks electric currents flowing in the Scrape-Off Layer (SOL) are a frequently observed and well known feature. However, the convective heat flux carried by these currents is often assumed to be small compared to the total parallel heat flux. In this paper it is shown that in ASDEX Upgrade the electric current, which was measured by Langmuir probes at the outer target, can be several times larger than the ion saturation current in low density L- and H-mode discharges. Therefore they have to be taken into account when calculating the target heat flux from the Langmuir probe data. Moreover, a detailed analysis reveals that for low density L- and H-mode discharges the heat flux profile is mainly determined by the current profile. By applying a 1D heat flux transport model it is demonstrated that the electric current can carry a large fraction (> 50 %) of the electron heat flux along the SOL convectively. Thus a Spitzer-Harm approach, where it is assumed that heat is transported only conductively, might not be valid in the investigated regime.