The development of effective closed-loop control algorithms is one of the main challenges in Additive Manufacturing (AM). Many parameters of AM processes need continuous monitoring and regulation, with temperature being one of the most important. We investigate the design of an output-feedback controller of the temperature process within the extruder of a Fused Deposition Modelling (FDM) AM system. Based on a state space approach, and using input-output measurements, we first design a model-based linear quadratic tracking controller, followed by an equivalent model-free, data-driven version. We demonstrate these approaches using a simulator of the temperature evolution in the extruder of the AM system, based on a model validated and identified in recent literature. Our findings show that a comparable performance to the model-based case is possible using only measured data, generated through probing control explorations during the simulations.