•Discussed those effects and presents literature regarding the known effects and data.•Presents a new procedure to easily determine the emissivity.•Presents a new calibration approach to consider effects of angle of view (introduced by e.g. curved surfaces).•Validates the new approach with an experiment.•Presents an error estimation. Infrared Thermography is a capable tool for resolving surface temperatures with high resolution and accuracy, even on complex surfaces. With current calibration techniques, the surface emissivity needs to be constant and close to unity to ensure a low calibration error. This is commonly achieved with special surface coatings. These coatings however, show a reduction of emissivity with increasing angle of view. Performing a state of the art in situ calibration with temperature calibration points (e.g. thermocouples) thus can lead to a measurement error on curved surfaces when assuming constant emissivity. In this paper, an adapted calibration procedure is presented considering the effects of surface topology. The process is closely linked to the basic in situ calibration with only few additional steps needed. If the angle of view θ(e. g. the camera position) is known in the experiment, this new procedure allows a correction of the induced effects and thus a reduction of measurement uncertainty. This can be achieved by only using a single additional in situ calibration pair. Data from a validation experiment is presented for two different camera systems (MWIR, LWIR), showing that the error can be reduced from ΔTS,rel>5% to ΔTS,rel<1.5% at θ≈65°, allowing the acquisition of temperature data on complex surfaces. With exact emissivity functions and camera positions, temperature acquisition can even be performed up to angles of view of θ≈80° with tolerable error.