The solar wind protons are accelerated to supersonic velocities within the distance of 10 solar radii from the Sun, as a consequence of a complex physical mechanism including particle kinetic effects as well as the field-particle energy and momentum exchange. We use a numerical kinetic model of the solar wind, accounting for Coulomb collisions (BiCoP), and model a solar wind accelerated only by the \emph{ambipolar} electrostatic filed ($E$) arising due to the difference in mass between electron and proton, and assuring quasi-neutrality and zero current. We study the effect $E$, which was found to be on the order of Dreicer electric field ($E_D$) \cite{Dreicer1959}, has on the resulting electron velocity distribution functions (VDF). The strahl electron radial evolution is represented by means of its \emph{pitch-angle width} (PAW), and the \emph{strahl parallel temperature} ($T_{s,\parallel}$). A continuous transition between collisional and weakly collisional regime results in broader PAW, compared to the single-exobase prediction imposed by the exospheric models. Collisions were found to scatter strahl electrons below 250 eV, which in turn has an effect on the measured $T_{s,\parallel}$. A slight increase was found in $T_{s,\parallel}$ with radial distance, and was stronger for the more collisional run. We estimate that the coronal electron temperature inferred from the observations of $T_{s,\parallel}$ in the solar wind, would be overestimated for between 8 and 15\%.