Current-conduction/transport mechanisms (CCMs or CTMs) through barrier and barrier height (BH) formation in the Al/(CdZnO)/p-Si/Al diodes, which were prepared by the sol-gel method, were examined in the range of 110-380 K. The decrease of zero-bias BH (Phi(Bo)) and increase of ideality factor (n) with decreasing temperature were observed. The classic Richardson plot indicated two distinct linear regions that correspond to low and high temperature range (LTR and HTR), respectively. Contrary to this, the acquired Richardson constant value (A*) was much lower than its theoretical value (32 A cm(-2) K-2). Such abnormal behavior of the Phi(Bo), n and A* was attributed to the evidence of the barrier inhomogeneities, especially at low temperature. Therefore, the Phi(Bo-)n, Phi(Bo) and (n(-1) - n) versus q/2kT plots were sketched to acquire significant clues for the Gaussian distribution (GD) of the BHs at rectifier contact area with the mean BH ((Phi) over bar (Bo)) and standard deviation (sigma(so)), which also have two linear parts with distinct slopes. (Phi) over bar and sigma(so) were calculated from the slope and intercept of Phi(Bo) versus q/2kT plot as 0.802 eV and 0.066 V for LTR, 1.043 eV and 0.106 V for HTR, respectively. The (Phi) over bar (Bo) and A* were acquired by utilizing the sigma(so) values and using the Richardson plot as 0.626 eV and 14.26 A cm(-2) K-2 for LTR and 1.021 eV and 32.53 A cm(-2) K-2 for HTR, respectively. Thus, the I-V-T characteristics of the Al/(CdZnO)/p-Si/Al diodes at forward biases were successfully elucidated by the double-GD of BHs with mean BHs of 0.626 eV and 1.021 eV, respectively.