Recently reported measurements of specific heat on the compound Mn-formate di-Urea by Takeda [Phys. Rev. B 63, 024425 (2001)] are considered. As a model to describe the overall thermodynamic behavior of such a compound, the easy-axis two-dimensional Heisenberg antiferromagnet is proposed and studied by means of the pure quantum self-consistent harmonic approximation. In particular, it is shown that when the temperature decreases, the compound exhibits a crossover from two-dimensional (2D) Heisenberg to 2D-Ising behavior, followed by a 2D-Ising-type phase transition, whose location allows one to get a reliable estimate of the easy-axis anisotropy driving the transition itself. Below the critical temperature T-N=3.77 K, the specific heat is well described by the two-dimensional easy-axis model down to a temperature T*=1.57 K, where a T-3 law sets in, possibly marking a low-temperature crossover of magnetic fluctuations from two to three dimensions.