Steelmaking is a high-temperature process, making it one of the industries that use refractories the most, especially for constructing steel ladles. Ladles are vessels used for transporting and refining molten steel in secondary metallurgy. Proper thermal management for the ladle is essential to reduce the risk of thermal shock to the refractory linings caused by steel tapping, which can lead to ladle breakouts. Additionally, the steel temperature is influenced by refractory linings’ temperature, particularly the ladle’s hot face. Therefore, tracking the temperature profile of ladles is necessary to achieve safe and cost-effective operations. Direct measurement with thermocouples of the refractory linings' temperature in each cycle is expensive, leading steel plants to use mathematical models, such as Computational Fluid Dynamics models, to monitor the temperature of the ladle’s refractory linings. However, these models often provide temperature data for every layer of the ladle, complicating interpretation and slowing subsequent calculations. This research project considers a finite volume model for predicting the temperature of refractory layers, developed at ArcelorMittal R&D. In this model, the temperature is simulated for 108 layers across the wall, bottom, and cover, highlighting the problem's high dimensionality. We present two model reduction methods, Proper Orthogonal Decomposition as a traditional and AutoEncoders as a machine learning approach, to obtain a reduced temperature profile of the ladle and compare these approaches. These methods can be used in further applications, online temperature prediction and heating estimation to manage refractories’ lifetime and reduce CO2 emissions.