The partially clamped piezoelectric crystal decreases the symmetry of its polarization response to the thermal and elastic excitation. As a result it acquires a pyroelectricity and volume piezoeffect even in the case of scalar perturbation. The temperature dependence of such artificial pyroelectric response was used to obtain the components of intrinsic polarization P(i), which is totally self-compensated in free piezoelectric crystal. For example quartz has P1 congruent-to 0.2 muC cm-2 at 300 K, which linearly decreases with temperature P approximately (theta - T) and vanishes at alpha - beta transition (theta = 846 K). The paraelectric phase of KDP crystal shows P3 approximately (theta -T)2 where theta = 484 K characterizes the high temperature phase transition.