Bayesian inference is commonly used for parameter estimation in physical processes such as heat conduction, radiation, and convection. In this paper, we introduce a robust solution framework for inverse heat conduction problems (IHCP) that combines Bayesian optimization modeling with Hamilton Monte Carlo (HMC) sampling techniques. To overcome the computational bottleneck of Bayesian methods in solving large-scale three-dimensional (3D) inverse problems, we accelerate the framework with high throughput and dimensionality reduction processing. The proposed framework is successfully applied to solve the IHCP from a pool boiling experiment and achieves computational efficiency 55 times higher than traditional Markov Chain Monte Carlo (MCMC) algorithms while maintaining equivalent solving accuracy in numerical simulations.