A Digital Twin in additive manufacturing enables real-time process control and optimization by creating a virtual representation of the physical counterpart. For Directed Energy Deposition (DED), this ideally requires the adoption of high-fidelity physics-based models to enable an accurate mapping from process parameters to the process conditions and ultimately to the deposited part properties. However, the complexity of the physics involved in DED makes its simulation challenging and prohibitively expensive, making real-time applications impossible. This motivates the development of fast-to-evaluate surrogate models [1]. This study focuses on the thermal aspects of the DED process and aims to introduce a data-driven surrogate model for high-fidelity thermal analysis. A Neural Operator is trained to resolve the temperature distribution in the heat-affected zone near the laser heat source. The operator learns the underlying physics from a training dataset generated by finite element simulations using codes (and underlying physics-based models) developed by CIMNE [2], covering a wide range of DED process parameters. Once trained, the Neural Operator enables accurate and computationally efficient temperature predictions [3] for the heat-affected zone of DED. Full scale temperature predictions are achieved by a dynamic one-way coupling, which maps the boundary conditions of the local model from the global temperature field, ensuring that local predictions remain consistent with the evolving temperature state of the full-scale part. This work represents a first step towards the final goal of bridging the gap between high-fidelity simulations and real-time applicability in DED processes.