Abstract <p>The results of numerical simulation using a modified Monte Carlo method with a heat bath algorithm for the pseudospin model of cuprates are presented. The temperature phase diagrams are constructed for various degrees of doping and for various parameters of the model, and the effect of local correlations on the critical temperatures of the model cuprate is investigated. It is shown that, in qualitative agreement with the results of the mean field approximaton, the heat bath algorithm leads to a significant decrease in the estimate of critical temperatures due to more complete accounting for fluctuations, and also makes it possible to detect phase inhomogeneous states. The possibility of using machine learning to accelerate the heat bath algorithm is discussed.</p>