This paper considers viscous fluid flow in a slot between two parallel plates which start inclining with respect to the horizontal line. The lower plate was heated and had nonhomogeneous temperature distribution while the upper plate was cooled and with homogeneous temperature distribution. The spatially periodic temperature distribution was gradually applied at the lower plate, after which the plates were slowly inclined in the positive-counterclockwise direction, and the fields of vorticity, streamfunction and temperature are pesented for different values of the angle of inclination. We used the vorticity-streamfunction formulation of Navier-Stokes equations, Fourier-Galerkin and Chebyshev collocation method for numerical simulation of 2D viscous fluid flow. We carried out numerical simulation using our in-house Matlab code for subcritical uniform Rayleigh number Rauni, and periodic Rayleigh number Rap on the lower plate. An accurate numerical scheme was developed to capture the full time-dependent behavior here. The interest lied in how the intensities of the vortexes and convection rolls changed as the inclination angle was increased with respect to time. Convection rolls rotating in the clockwise direction expanded and the rolls rotating in the counterclockwise direction shrank and their centers moved closer to the lower wall. Thermal drift appeared between them when the inclination angle started increasing.