The digitalization of manufacturing processes offers great potential in quality control, traceability, and the planning and setup of production. In this regard, process simulation is a well-known technology and a key step in the design of manufacturing processes. However, process simulations are computationally and time-expensive, typically beyond the manufacturing-cycle time, severely limiting their usefulness in real-time process control. Machine Learning-based surrogate models can overcome these drawbacks, and offer the possibility to achieve a soft real-time response, which can be potentially developed into full close-loop manufacturing systems, at a computational cost that can be realistically implemented in an industrial setting. This paper explores the novel concept of using a surrogate model to analyze the case of the press hardening of a steel sheet of 22MnB5. This hot sheet metal forming process involves a crucial heat treatment step, directly related to the final part quality. Given its common use in high-responsibility automobile parts, this process is an interesting candidate for digitalization in order to ensure production quality and traceability. A comparison of different data and model training strategies is presented. Finite element simulations for a transient heat transfer analysis are performed with ABAQUS software and they are used for the training data generation to effectively implement a ML-based surrogate model capable of predicting key process outputs for entire batch productions. The resulting final surrogate predicts the behavior and evolution of the most important temperature variables of the process in a wide range of scenarios, with a mean absolute error around 3 °C, but reducing the time four orders of magnitude with respect to the simulations. Moreover, the methodology presented is not only relevant for manufacturing purposes, but can be a technology enabler for advanced systems, such as digital twins and autonomous process control.