We study the two dimensional quantum Heisenberg antiferromagnet on the square lattice with easy-axis exchange anisotropy by the semiclassical method called pure-quantum self-consistent harmonic approximation. In particular, we focus on the problem of the existence of a nite-temperature transition in such a model, and study the corresponding critical temperature as the spin value and the anisotropy vary. We find that an Ising-like transition characterizes the model even when the anisotropy is of the order of 10-2J (J being the intra-layer exchange integral). The good agreement found between our theoretical results and the experimental data for the compounds Rb2MnF4, K2MnF4, and K2NiF4 shows that the insertion of the easy-axis exchange anisotropy, with quantum effects properly taken into account, provides a quantitative description and explanation of the real system's critical behaviour.