Temperature-activated charge transport in disordered organic semiconductors at large carrier concentrations, especially relevant in organic field-effect transistors (OFETs), has been thoroughly considered using a recently developed analytical formalism assuming a Gaussian density-of-states (DOS) distribution and Miller-Abrahams jump rates. We demonstrate that the apparent Meyer-Neldel compensation rule (MNR) is recovered regarding the temperature dependences of the charge carrier mobility upon varying the carrier concentration but not regarding varying the width of the DOS. We show that establishment of the MNR is a characteristic signature of hopping transport in a random system with variable carrier concentration. The polaron formation was not involved to rationalize this phenomenon. The MNR effect has been studied in a OFET based on C-60 films, a material with negligible electron-phonon coupling, and successfully described by the present model. We show that this phenomenon is entirely due to the evolution of the occupational DOS profile upon increasing carrier concentration and this mechanism is specific to materials with Gaussian-shaped DOS. The suggested model provides compact analytical relations which can be readily used for the evaluation of important material parameters from experimentally accessible data on temperature dependence of the mobility in organic electronic devices. Experimental results on temperature-dependent charge mobility reported before for organic semiconductors by other authors can be well interpreted by using the model presented in this paper. In addition, the presented analytical formalism predicts a transition to a Mott-type charge carrier hopping regime at very low temperatures, which also manifests a MNR effect.