A model of a turbulent axisymmetric thermal rising in an atmosphere with altitude-dependent density is proposed. A numerical study of the thermal is performed for an isothermal atmosphere with exponentially decreasing density. The structure of the thermal corresponding to the square-root law of the ascent is obtained in similarity coordinates. An analytical solution is found for a wide class of the density variation functions and studied in detail for an inverse-square law of density diminution with height. It is shown that as the thermal penetrates the low-density atmospheric layers, its top edge becomes less sharp and the width of the thermal increases. However, the self-similar coordinate of the cloud top remains almost constant and the square-root law of the ascent still holds.