Thermally stimulated current (TSC) is a widely used technique to assess trap states and extract their density, energy, and capture rate using analytical expressions. In many cases, the latter are derived from physical models pertaining to inorganic semiconductors stipulating the absence of space charge or constant lifetime of free charge carriers. Especially for organic semiconductors, the validity of these equations can, therefore, be argued. Here, we investigate the validity range of this approach by fitting the classical equations to synthetic TSC data obtained from drift-diffusion simulation using representative input parameters for organic semiconductors. We find that the equation derived for slow recapture rate as well as the initial rise method provide excellent trap parameter predictions. On the other hand, the equation using the temperature of the peak current as well as the one derived for fast retrapping have a limited range of validity. An important merit of drift-diffusion modeling is the possibility to access local variables such as charge carrier density, electric field, and recombinaton. We unravel that a small fraction of traps nearby the electrode cannot be emptied even at high temperature due to the diffusion of charge carriers from the electrode into the semiconductor. Additionally, we find that an important electrostatic factor relates the extracted charge carriers measured by the external circuit and the input trap density. For the homogeneously distributed trap states used here, this factor is precisely two. Finally, extensions of the model are analyzed by implementing temperature and field dependent mobility into the drift-diffusion model. Published under an exclusive license by AIP Publishing.