Due to its ability in producing pieces of complex geometry whilst avoiding polymerisation in an au- toclave, the Automated Fibre Placement (AFP) is a promising solution to face the increasing needs of composite materials. In order to optimize this process the first step is to models it in an efficient way. In the last decade, the increasing interest in Reduced Order Modelling allowed the development of many efficient techniques for solving science and engineering problems. One of the pioneer methods, the Proper Orthogonal Decomposition, has been widely used for different engineering applications, but the sampling step of the method remains nowadays a limiting stage in terms of storage and CPU time efficiency. More recently, the Proper Generalized Decomposition - a method based on the use of separated representations - allowed to treat high dimensional problems arising from multidimensional physics, see [1] for a recent review. Many works are carried out, in particular at the Ecole ́ Centrale in Nantes, using such a method; see for example [2, 3]. In our work, we develop a multi-parametric model in order to solve the heat equation, involving a displacement of the heat source. This movement of the laser beam is drown with a varying velocity. The hyper-cube of solution could then be used on-line in a control loop.