In most additive manufacturing (AM) processes, elongated beads are assembled to form 3D parts. Recently, a mechanical model named QuadWire, dedicated to efficient simulations of such processes, has been proposed [1] and validated against experimental digital image correlation [1]. QuadWire is an extended 1D model, allowing the use of elongated discretizations for efficient meshing without conditioning issues. It uses 4 particles per material point to capture complex 3D mechanical states, while significantly reducing computation time compared to conventional approaches [3]. However, previous contributions were limited to the mechanical behavior. In this contribution, capitalizing on the potential for computation cost reduction of this extended 1D framework, a thermodynamic analysis is provided to derive the heat equation of the QuadWire model. Four coupled heat equations are derived, corresponding to the 4 temperatures per material point, which are re-written into 4 uncoupled heat equations using the average temperature of the 4 particles, and temperature differences between the particles. In addition, the Finite Element discretization with a Runge-Kutta time discretization scheme is detailed for practical applications. This approach enables the simulation to overcome limitations of other fast thermal simulation tools used in AM. For instance, a fast modeling approach [4], validated experimentally against various experiments [5-7] was limited to single track geometry, whereas the QuadWire approach enables the simulation of complex fully 3D parts, while maintaining reduced computation cost.