It is commonly believed that a 2D quantum memory cannot be self-correcting, in the sense that, when exposed to a thermal bath, its relaxation time will be bounded as a function of the system size. In this talk, I will present some recent results that confirm this belief, for the case of 2D Kitaev's quantum double models. The proof of this result is based on a representation of the Gibbs state of the quantum double models as a PEPS, which allows us to rigorously estimate the spectral gap of the correspoding parent Hamiltonian.