The thermophoretic force on dust particles is caused by a temperature gradient in the background gas. This force can be important in experiments or production processes and in other environments where dust occurs. We discuss the local cooling of the neutral gas by levitated dust clouds and how this affects the temperature gradient and the equilibrium dust density profile. Dust is heated through neutral gas particle impacts while it loses energy by either reemitting impacting particles or by thermal radiation at the particle temperature. The dust particle temperature can be considerably lower than that of the ambient gas and can therefore lead to a local cooling of the gas. Changes in the temperature gradient and the thermophoretic force can be large enough to affect the equilibrium density profile of levitated dust. We find that the equilibrium profile with the thermophoretic force calculated from the temperature profile without dust cooling is closer to the electrode but with much the same shape as the profile calculated without the thermophoretic force. The profile where local cooling is included in the thermophoretic force is more compressed compared to the profile without local cooling and it often has a pronounced peak closest to the electrode. Since radiation cooling of a dust particle is proportional to the fourth power of its temperature, the cooling effect is largest at comparatively high gas (and dust) temperatures. We show examples of levitated dust layer profiles with and without the dust cooling effect.