The purpose of this paper is determination the critical geometric dimensions of a three-dimensional vertical heated cavern. In this rate the convection's contribution to heat transfer will be limited due to thermal conductivity at a fixture temperature drop. The model validated and verified by comparison with the experimental results. А stable non-stationary flow regime is observed for Rayleigh number Ra = 15,000, because the temperature fields in different cross-sections of the flow coincide. For the flow with Rayleigh number Ra = 15,000, the nonstationary formulation without the turbulence model did not give the required convergence on residuals. So it was calculated by using the three-dimensional RANS approach closed with the k-w SST turbulence model. In this case the flow is unstable in the third direction, therefore it is impossible to consider the cavern as a heat insulator at numbers Ra = 10,000 and above.