This paper shows numerically the formation of secondary whirls embedded in axisymmetric vertical vortices generated in a cylindrical annulus non-homogeneously heated from below. This secondary circulation, that is formed near the center of the primary vortex, appears after a thermoconvective instability. The transition from the axisymmetric vortex to the time-dependent flow where the subvortex is found is studied using nonlinear simulations. The size of the inner radius of the cylindrical annulus is relevant for the appearance or not of subvortices. They only form for small and medium values of the inner radius. The temperature profile at the bottom affects the intensity of the subvortex generated. Results are remarkable as they qualitatively describe observations in dust devils.