This study presents electrical characteristics of n-GaAs based Schottky barrier diodes (SBDs) with Rhenium (Re) rectifier contacts. The electrical characteristics of the Re/n-GaAs SBDs were investigated utilizing the forward bias current-voltage (IF-VF) data collected in temperature range of 60-400 K. The values of ideality factor (n) and zero-bias barrier height (ΦBo) were found as 9.10 and 0.11 eV for 60 K, and 1.384 and 0.624 eV for 400 K, respectively, on the basis of thermionic-emission theory. The conventional Richardson plot deviated from linearity at low temperatures and the Richardson constant value (A*) was obtained quite lower than the theoretical value for this semiconductor (8.16 A cm-2 K-2). nkT/q-kT/q plot shows that the field-emission may be dominant mechanism at low temperatures as a result of tunneling via surface states since the studied n-GaAs’s doping concentration is on the order of 1018 cm-3, i.e. at high values so leads to tunneling. On the other hand, ΦBo-n, ΦBo-q/2kT and (n-1-1)-q/2kT plots exhibit linearity but this linearity is observed for two temperature regions (60-160 K and 180-400 K) due the presence of double Gaussian distribution (GD) of the barrier height. Therefore, the standard deviation value was obtained from the plot of ΦBo-q/2kT and it was used for modifying the conventional Richardson plot into the modified Richardson plot by which the values of mean barrier height and A* were obtained as 0.386 eV and 15.55 A cm-2 K-2 and 0.878 eV and 8.35 A cm-2 K-2 for the low and high temperature regions, respectively. As a result, IF-VF-T characteristics of the Re/n-GaAs SBDs were successfully elucidated by double-GD of barrier height.