Wire-arc direct-energy deposition has emerged as a promising additive manufacturing methodology. However, the complex thermal dynamics inherent to the process present challenges in ensuring the structural integrity and mechanical properties of fabricated components. Finite element method (FEM) simulations have been conventionally employed to predict the thermal history during deposition; yet, their high computational demand increases significantly with scale. Given the necessity of multiple, repetitive simulations for heat management and the determination of optimal printing strategies, FEM simulation quickly becomes impractical. Instead, advancements have been made in using trained neural networks as surrogate models for rapid prediction. Nevertheless, traditional data-driven approaches necessitate large amounts of relevant and verifiable external data, either from simulation, experimentation, or analytical solutions, during the training and validation of the neural network. The introduction of physics-informed neural networks (PINNs) has opened up an alternative simulation strategy by leveraging existing knowledge of physical phenomena with advanced machine learning methods. While hybrid methods exist, a purely physics-informed neural network requires zero additional external data, limiting the necessary computational time to only the model training time. This study successfully implemented and refined a PINN for this purpose in a 4D domain, capable of outperforming FEM simulation on commercial hardware in wall-clock time by 62.5% and 98.6%, depending on the desired grid resolution, with a relative L² error of 7.267e-2.