The study of temperature dependence of the sublattice magnetization in the quasi-two-dimensional $S=\frac{1}{2}$ cuprate antiferromagnets was inspired by the existing experimental evidence concerning sublattice magnetization temperature dependence, both in the vicinity of absolute zero for the high-$T_C$ parent compound ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ and in the whole temperature region from absolute zero to the Néel temperature $\left(T_N\right)$ for ${\mathrm{La}}_2\mathrm{Cu}{\mathrm{O}}_4$ and $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.15}$. Using the spin Green’s functions method for the quantum Heisenberg antiferromagnetic model, we obtain the results which show excellent agreement with the experimental data, proving that in the wide temperature region (from 0 to $T_N$), this method is more appropriate than the harmonic spin-wave theory and Schwinger-boson mean-field theory.