The evolution of the electron heat flux in the solar wind is regulated by the interplay between several effects: solar wind expansion, which can potentially drive velocity–space instabilities, turbulence, wave–particle interactions, and, possibly, collisions. Here we address the respective role played by the solar wind expansion and the electron firehose instability (EFI), developing in the presence of multiple electron populations, in regulating the heat flux. We carry out fully kinetic, expanding box model simulations and separately analyze the enthalpy, bulk, and velocity distribution function skewness contributions for each of the electron species. We observe that the key factor determining electron energy flux evolution is the reduction of the drift velocity of the electron populations in the rest frame of the solar wind. In our simulations, redistribution of the electron thermal energy from the parallel to the perpendicular direction after the onset of the EFI is observed. However, this process seems to impact energy flux evolution only minimally. Hence, reduction of the electron species drift velocity in the solar wind frame appears to directly correlate with efficiency for heat flux instabilities.