Efficient glass production depends on the continuous supply of heat from the glass melt to the floating layer of batch, or cold cap. Computational fluid dynamics (CFD) are employed to investigate the formation and behavior of gas cavities that form beneath the batch by gases released from the collapsing primary foam bubbles, ascending secondary bubbles, and in the case of forced bubbling, from the rising bubbling gas. The gas phase fraction, temperature, and velocity distributions below the cold cap are used to calculate local and average heat transfer rates as a function of the bubbling rate. It is shown that the thickness of the cavities is nearly independent of the cold cap shape and the amount of foam evolved during batch conversion. It is ~7 mm and up to ~15 mm for the cases without and with forced bubbling used to promote circulation within the melt, respectively. Using computed velocity and temperature profiles, the melting rate of the simulated high‐level nuclear waste glass batch was estimated to increase with the bubbling rate to the power of ~0.3 to 0.9, depending on the flow pattern. The simulation results are in good agreement with experimental data from laboratory‐ and pilot‐scale melter tests.