  We investigate stability properties of the radially symmetric solution
corresponding to the vortex defect (so called "melting hedgehog") in the
framework of the Landau - de Gennes model of nematic liquid crystals. We prove
local stability of the melting hedgehog under arbitrary $Q$-tensor valued
perturbations in the temperature regime near the critical supercooling
temperature. As a consequence of our method, we also rediscover the loss of
stability of the vortex defect in the deep nematic regime.
