The theoretical description of the reorientational dynamics in a microized liquid crystal cell, where the nematic sample is confined by two horizontal and two lateral surfaces, under the influence of a temperature gradient ∇T is presented. We have carried out a numerical study of the system of hydrodynamic equations including director reorientation, fluid flow v, and the temperature redistribution across the cell under the influence of ∇T, when the sample is heated both from below and from above. Calculations show that, due to interaction between the gradient of the director field ∇ and ∇T, the bidirectionally aligned liquid crystal (BALC) sample settles down to a stationary bi-vortical flow regime. As for a nematogenic material, we have considered the BALC cell to be occupied by 4-n-pentyl-4′-cyanobiphenyl, and investigated the effect of both ∇ and ∇T on the magnitude and direction of v, for a number of hydrodynamic regimes.