  This study investigates the predictive capabilities of common DFT methods
(GGA, GGA+$U$, and GGA+$U$+$V$) for determining the transition temperature of
antiferromagnetic insulators. We utilize a dataset of 29 compounds and derive
Heisenberg exchanges based on DFT total energies of different magnetic
configurations. To obtain exchange parameters within a supercell, we have
devised an innovative method that utilizes null space analysis to identify and
address the limitations imposed by the supercell on these exchange parameters.
With obtained exchanges, we construct Heisenberg Hamiltonian to compute
Transition temperatures using classical Monte Carlo simulations. To refine the
calculations, we apply linear response theory to compute on-site ($U$) and
intersite ($V$) corrections through a self-consistent process. Our findings
reveal that GGA significantly overestimates the transition temperature (by
~113%), while GGA+$U$ underestimates it (by ~53%). To improve GGA+$U$ results,
we propose adjusting the DFT results with the $(S+1)/S$ coefficient to
compensate for quantum effects in Monte Carlo simulation, resulting in a
reduced error of 44%. Additionally, we discover a high Pearson correlation
coefficient of approximately 0.92 between the transition temperatures
calculated using the GGA+$U$ method and the experimentally determined
transition temperatures. Furthermore, we explore the impact of geometry
optimization on a subset of samples. Using consistent structures with GGA+U and
GGA+U+V theories reduced the error.
