We analyze the growth of a droplet of a stable phase (a plane wave front in one-dimensional case) under strong supercooling in the framework of the Landau-Ginzburg potential for both a conserved and a nonconserved order parameter coupled to thermal diffusion. When the coupling between changes in temperature and the order parameter is strong enough, and the heat conductivity is sufficiently small, the following nontrivial phenomenon may occur: the latent heat released with the growth of a droplet is taken away very slowly, and the local overheating transforms the initially overcooled state into an overheated one. As a result, the rate of droplet growth decreases, and even may change its sign, so that droplets of radius larger than the critical one, nevertheless, may shrink. For the steady-state growth in the one-dimensional case this phenomenon was analyzed analytically, while beyond the steady regime and in the two-dimensional case, the equations were solved numerically. The presence of a thermal bath with heat loss through thermal dissipation narrows the areas of occurence of this phenomenon.