  We develop a method of non-perturbative optical control over adiabatic
remagnetisation of the nuclear spin system and apply it to verify the spin
temperature concept in GaAs microcavities. The nuclear spin system is shown to
exactly follow the predictions of the spin-temperature theory, despite the
quadrupole interaction that was earlier reported to disrupt nuclear spin
thermalisation. These findings open a way to deep cooling of nuclear spins in
semiconductor structures, with a prospect of realisation of nuclear
spin-ordered statesfor high fidelity spin-photon interfaces.
