Assuring the quality of the finished workpieces is one of the major challenges in metal AM. In this regard, it has been shown that material properties are strongly linked to the temperature field and cooling rate of the workpiece during the production process [1]. Throughout the last decade multiple efforts have been aimed at developing control-oriented temperature models to obtain the desired material properties through the manipulation of process parameters. Whilst many such models focus on the localised control of temperature and/or cooling rate, such approaches have limitations in their ability to guarantee uniformity throughout the workpiece [2]. The need to model the temperature for the entire workpiece has thus emerged. This contribution presents two different spatio-temporal models of the temperature on the entirety of the workpiece surface. The models have been identified and validated using high speed (300Hz) infrared camera data from real-life experiments bonding AISI 316 L powder (workpiece) to a S235 steel substrate through direct laser deposition (DLD). Before the thermal data is used for system identification, it goes through several image processing steps including rectification, melt-pool and track detection, spatial discretization and (for the second case study) emissivity correction. The heat transfer equation is used as physical basis for both grey-box models. In the first case study, simplified assumptions lead to the development of a linear parameter-varying (LPV) model of the temperature of a workpiece consisting of a single horizontal layer [3]. The second case study extends the modelling task to multi-layer samples and develops a model that accounts for the growth of the workpiece [4]. In both studies a good prediction quality is achieved: when considering the horizontal workpiece (the only direct comparison possible), the validation BFR is 67% for the first and 62% for the second case study.