In this paper, we propose two novel generalized belief propagation (BP) algorithms to improve the convergence behavior of the conventional BP algorithm. By incorporating a dynamic temperature into the free energy formulation, message passing is performed on a dynamic surface of energy cost. The proposed cooling process helps BP converge to a stable fixed point with a lower energy value that leads to better estimations. For decoding turbo-like error correcting codes, we adopt a parametric Gaussian approximation to relax the binary parity check constraints and generalize the conventional binary networks as well. Both the computational complexity and the convergence rate of the proposed annealed BP algorithms are almost the same as those of the conventional BP algorithm. Simulated performance of the proposed algorithms when they are used to decode a low density parity check (LDPC) code and the (23,12) Golay code is presented to validate our proposals.