The theoretical description of the reorientational dynamics and the relaxation processes in the hybrid-oriented compressible liquid crystal (HOCLC) cell under the influence of the vertical temperature gradient has been presented. We have carried out a numerical study of the system of hydrodynamic equations including director reorientation, fluid flow, and both the temperature and density redistribution across a HOCLC cell under the influence of a temperature gradient del T directed normal to the restricting surfaces, when the sample was heated both from below and above. Calculations show that, under the influence of del T, the HOCLC sample settles down to a stationary flow regime, both with the horizontal u and vertical w components of velocity v, and u is directed in the opposite direction, with, approximately, one order of the magnitude less, than one in the case of the incompressible hybrid-oriented liquid crystal cell. The role of hydrodynamic flow in the relaxation processes of the stress tensor components, for a number of dynamic regimes in a HOCLC cell containing 4-n-pentyl-4'-cyanobiphenyl, has been investigated. (C) 2009 Elsevier B.V. All rights reserved.