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It has been previously shown (Phys. Rev. E 66, 066305, 2002) that a non-rotating turbulent convection with nonuniform large-scale flows contributes to the turbulent heat flux. As a result, the turbulent heat flux depends explicitly not only on the gradients of the large-scale temperature, but it also depends on the gradients of the large-scale velocity. This is because the nonuniform large-scale flows produce anisotropic velocity fluctuations which modify the turbulent heat flux. This effect causes an excitation of a convective-wind instability and formation of large-scale semi-organised coherent structures (large-scale convective cells). We perform mean-field numerical simulations of shear-free convection which take into account the modification of the turbulent heat flux by nonuniform large-scale flows. The redistribution of the turbulent heat flux by the nonuniform large-scale motions in turbulent convection plays a crucial role in the formation of the large-scale semi-organised coherent structures. This effect results in a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale convective cells. The convective-wind instability is excited when the scale separation ratio between the height of the convective layer and the integral turbulence scale is large. The level of the mean kinetic energy at saturation increases with the scale separation ratio. Inside the large-scale convective cells, there are local regions with the positive vertical gradient of the potential temperature which implies that these regions are stably stratified.