Wire Arc Additive Manufacturing (WAAM) is a rising metal additive manufacturing technology. Having access to a real-time simulation of the WAAM process is an increasing challenge since it would make it possible to do live monitoring or to more efficiently adjust process parameters during the CAM operations. One major difficulty to overcome to create a real-time simulation is the importance of thermal conditions. Numerous works showed that thermal conditions of the manufactured part during the process have a direct impact on the quality and the geometry of the part. At the same time, it is a well-known fact that precise thermal simulations in complex and evolving conditions are much slower than real time. The proposed approach is based on the idea that defects happen only when the thermal conditions are far from their usual value. Under this assumption, a real-time approximative thermal simulation is sufficient to simulate the thermal side of the WAAM process. Such a simulation, which is a first step in simulating in real time the whole WAAM process, is proposed in this paper.