Laser-based Powder Bed Fusion of Metals (PBF-LB/M) is an additive manufacturing technology suitable for producing metal components with complex geometries and remarkable mechanical performances. The geometrical complexity of parts produced using PBF-LB/M technology calls for flexible numerical approaches. Therefore, in such a context, immersed boundary methods seem to offer a valid alternative to the traditional mesh-conforming Finite Element Method (FEM). In the present contribution, the multi-level hp version of FEM is employed to achieve local refinement while an immersed boundary approach, namely the Finite Cell Method (FCM), is used to implicitly capture the material interface between air, powder, and solid material states, avoiding conform meshing. We present and experimentally validate a high-fidelity thermal model suitable to describe temperature evolution during PBF-LB/M processes of Stainless Steel 316L material in an FCM setting. The proposed thermal model is first calibrated and validated with respect to experimental measurements obtained by means of a coaxial short-wave infrared (SWIR) thermal camera for single laser tracks with powder. Successively, it is applied to investigate the temperature field evolution during the manufacturing process of complex cellular materials such as gyroids and octet lattice structures, comparing simulated thermal field with online data acquired using a mid-wave infrared (MWIR) thermal camera. Implementation of the presented numerical framework is publicly available at https://gitlab.com/hpfem/code/pbf under MIT-License, the code is also distributed as a Python library (pip install pbf).