A stochastic inverse heat transfer problem is formulated to determine the transient heat flux, treated as an unknown Neumann boundary condition. Consequently, an advanced extension of Ensemble Kalman Filtering technique is employed for concurrent temperature distribution prediction and heat flux estimation. This method integrates Radial Basis Functions to reduce the number of unknown inputs and alleviate the computational cost. The process is specifically applied to a mold in Continuous Casting machinery, leveraging sequential temperature data from thermocouples within the mold. Our research offers a significant advancement in achieving probabilistic boundary condition estimation in real-time, despite noisy measurements and model errors. Additionally, we highlight the procedure’s reliance on certain hyperparameters not previously documented in the literature. Accurate real-time heat flux prediction is crucial for the smooth operation of Continuous Casting machinery at the boundary where the mold and molten steel interface, which is otherwise not physically measurable. This development enables efficient real-time monitoring and control, essential for preventing caster shutdowns.