We present an investigation into the vertical transport through 13 different superlattice structures, where the well and barrier widths, doping concentration, dopant position, and contact layers were varied. Although superlattices have been extensively studied since 1970, there is a lack of publications on transport through superlattices similarly low doped as THz quantum cascade lasers (QCLs), for which the doping is in the 3-5×10^{10} cm^{-2} range. The superlattices presented are doped in the same range as THz QCLs, with contact layers and fabrication comparable to high-temperature THz QCLs. The temperature-dependent current-voltage characteristics were measured starting from 5 K and an anomalous temperature effect was observed at the first plateau. The measured current through the superlattice first decreases before increasing again with increasing temperature, resulting in the lowest current occurring at 75-110 K. This behavior is also observed in some THz QCLs. The effect disappears for thinner barriers, higher quantum well doping, or modified contact layers, indicating a strong dependency on band bending, due to the large difference in the doping of the contact layers and the superlattice, which is confirmed with multiscattering Büttiker simulations.