The magnitude and direction of the permanent electric polarization in the non-crystalline, polar phase (termed quasi-amorphous) of SrTiO3 in Si\SiO2\Me\SrTiO3\Me, (Me = Cr or W), Si\SrRuO3\SrTiO3, and Si\SrTiO3 layered structures were investigated. Three potential sources of the polarization which appears after the material is pulled through a temperature gradient were considered: a) contact potential difference; b) a flexoelectric effect due to a strain gradient caused by substrate curvature; and c) a flexoelectric effect due to the thermally induced strain gradient that develops while pulling through the steep temperature gradient. Measurements show that options a) and b) can be eliminated from consideration. In most cases studied in this (Si\SrTiO3, Si\SiO2\Me\SrTiO3\Me, M = Cr or W) and previous works (Si\BaTiO3, Si\BaZrO3), the top surface of the quasi-amorphous phase acquires a negative charge upon heating. However, in Si\SrRuO3\SrTiO3 structures the top surface acquires a positive charge upon heating. On the basis of the difference in the measured expansion of the upper and lower surfaces of the SrTiO3 layer in the presence and absence of SrRuO3, we contend that the magnitude and direction of the pyroelectric effect are determined by the out-of-plane gradient of the in-plane strain in the SrTiO3 layer while pulling through the temperature gradient.