In order to good interpret of temperature dependent main electrical parameters in Au/2% graphene–cobalt (GC) doped (Ca3Co4Ga0.001Ox)/n-Si structure, forward bias current–voltage (I–V) characteristics have been investigated in the temperature range of 80–340K. The possible current-conduction mechanisms (CCMs) in this structure was also investigate in detail. The ideality factor (n), reverse saturation current (Io), and zero-bias barrier height (ΦBo) values were found as 14.5, 7.2×10−6A, 0.141eV at 80K and 3.18, 1.7×10−3A, and 0.526eV at 340K, respectively. It is clear that both the value of n and ΦBo are strong function of temperature. While the value of n decreases with increasing temperature, ΦBo increases. In order to explain such behavior of BH the ΦBo and n, ΦBo vs q/2kT, ΦBo vs n, and (n−1−1) vs q/2kT plots were drawn to obtain an evidence of a Gaussian distribution (GD) of the BHs and it shows a straight line. The mean value of BH (Φ¯Bo) and standard deviation (σs) were found from the slope and intercept of this plot as 0.614eV and 0.088V, respectively. By using the modified Richardson plot, the Φ¯Bo and Richardson constant (A*) values were obtained from the slope and intercept of this plot as 0.604eV and 108.23Acm−2K−2, respectively. It is clear that this value of A* (=108.23Acm−2K−2) is very close to the theoretical value 112Acm−2K−2 for n-Si. In conclusion, the temperature dependence of the forward bias I–V characteristics of the structure can be successfully explained on the basis of a thermionic emission (TE) mechanism with GD of the BHs.