Industrialising manufacturing processes for aeronautic composite parts is a challenging issue. Among the existing techniques, the Automated Fibre Placement (AFP) is a promising one, since it allows the making of large and complex pieces with good productivity and repeatability. However, in order to ensure the regulatory requirements, the process must be controlled efficiently. In this paper, we propose the off-line computation of a parametric solution to a minimisation problem subject to heat equation. To solve this saddle-point problem with the so-called PGD method, we considered using Uzawa's technique or the Ideal Minimal Residual-based formulation, the aim being real-time control of the heat source within the AFP process.