Adequate preheating of the submerged entry nozzle (SEN) is important to avoid problems such as cracks and skulling, and depends on torch configuration, fuel, SEN geometry and other factors. A steady-state axisymmetric computational model of the flame, combustion reactions, and air entrainment has been combined with a transient model of heat transfer in the refractory walls to simulate the SEN preheating process. The model predictions match with experimental measurements of preheating with a natural-gas torch, including temperature profile across the flame, temperature histories measured inside the SEN wall, the flame shape, and the SEN outer wall temperature distribution. A simple spread-sheet model is introduced to accurately predict flame temperature, heat transfer coefficients and product properties for simple models of SEN preheating, given the air entrainment predicted from the combustion model. The results reveal the times required to reach adequate preheating temperature. Moreover, optimal positioning of the torch above the top of the SEN decreases ambient air entrainment, which increases the temperatures and shortens preheating time.