Schottky CdTe nuclear detectors are affected by bias-induced polarization phenomena when operating at room temperature. A space charge buildup occurs at the blocking contact causing the degradation in detection performance. By means of Pockels effect, we study the electric field distribution inside the detector and its variation with time and temperature. The analysis of the space charge has allowed us to point out the role of the Schottky contact and of carrier detrapping from deep levels in the polarization mechanism. Moreover, measured current transients have been quantitatively accounted for by the increase in the electric field at the blocking junction.