Predicting protein thermostability change upon mutation is crucial for understanding diseases and designing therapeutics. However, accurately estimating Gibbs free energy change of the protein remained a challenge. Some methods struggle to generalize on examples with no homology and produce uncalibrated predictions. Here we leverage advances in graph neural networks for protein feature extraction to tackle this structure–property prediction task. Our method, BayeStab, is then tested on four test datasets, including S669, S611, S350, and Myoglobin, showing high generalization and symmetry performance. Meanwhile, we apply concrete dropout enabled Bayesian neural networks to infer plausible models and estimate uncertainty. By decomposing the uncertainty into parts induced by data noise and model, we demonstrate that the probabilistic method allows insights into the inherent noise of the training datasets, which is closely relevant to the upper bound of the task. Finally, the BayeStab web server is created and can be found at: http://www.bayestab.com. The code for this work is available at: https://github.com/HongzhouTang/BayeStab.