Accurate real-time prediction of the heat flux is imperative for the smooth operation of Continuous Casting machinery at the boundary region where the Continuous Casting mold and the molten steel meet which is not also physically measurable. A stochastic inverse heat transfer problem is formulated to infer the transient heat flux, which is treated as an unknown Neumann boundary condition. Therefore, a Data Assimilation technique is utilized for simultaneous heat flux estimation and temperature distribution prediction based on the sequential availability of temperature provided by thermocouples inside the mold. This approach is also incorporated with Radial Basis Functions not only to lessen the size of unknown inputs but also to mitigate the computational burden of this technique. The procedure applies to the specific case of a mold used in Continuous Casting machinery. Our research represents a significant contribution to achieving probabilistic boundary condition estimation in real-time handling with noisy measurements and errors in the model. We additionally demonstrate the procedure’s dependence on some hyperparameters that are not documented in the existing literature. Thus, this paves the way for efficient real-time monitoring and control, which is critical for preventing caster shutdowns.