The efficiency of the adiabatic demagnetization of the nuclear spin system (NSS) of a solid is limited, if quadrupole effects are present. Nevertheless, despite a considerable quadrupole interaction, recent experiments validated the thermodynamic description of the NSS in GaAs. This suggests that nuclear spin temperature can be used as a probe of nuclear magnetic resonances. We implement this idea by analyzing the modification of the NSS temperature in response to an oscillating magnetic field at various frequencies, an approach termed as the warm-up spectroscopy. It is tested in a n-GaAs sample where both mechanical strain and built-in electric field may contribute to the quadrupole splitting, yielding the parameters of electric field gradient tensors for As75 and both Ga isotopes, Ga69 and Ga71.