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Quantum correlated pairs of photons of extremely different frequency ranges can be emitted by spontaneous parametric down-conversion process in the frequency non-degenerate regime, when the signal frequency is just slightly shifted from the pump one and the idler wave hits the terahertz range. We have measured frequency-angular distributions of the power of signal photons generated in the Stokes and anti-Stokes ranges in the wide range of temperatures of the nonlinear crystal, from 4 K up to 300 K. It is shown how the anti-Stokes signal reduces to zero at the lowest cryogenic temperatures, while in the anti-Stokes range the pure quantum contribution stays at all the temperatures. The temperature and spectral dependencies are analyzed using the nonlinear Kirchhoff law, with account of crystal terahertz absorption and thermal field fluctuations.