The accuracy of thermal conductivity measurements by the micro-Raman technique for suspended multi-layer graphene flakes has been shown to depend critically on the quality of the thermal contacts between the flakes and the metal electrodes used as the heat sink. The quality of the contacts can be improved by nonlocal laser annealing at increased power. The improvement of the thermal contacts to initially rough metal electrodes is attributed to local melting of the metal surface under laser heating, and increased area of real metal-graphene contact. Improvement of the thermal contacts between multi-layer graphene and a silicon oxide surface was also observed, with more efficient heat transfer from graphene as compared with the graphene-metal case.