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The placement of temperature sensitive and safety-critical components is crucial in the automotive industry. It is therefore inevitable, even at the design stage of new vehicles that these components are assessed for potential safety issues. However, with increasing number of design proposals, risk assessment quickly becomes expensive. We therefore present a parameterized surrogate model for the prediction of three-dimensional flow fields in aerothermal vehicle simulations. The proposed physics-informed neural network (PINN) design is aimed at learning families of flow solutions according to a geometric variation. In scope of this work, we could show that our nondimensional, multivariate scheme can be efficiently trained to predict the velocity and pressure distribution for different design scenarios and geometric scales. The proposed algorithm is based on a parametric minibatch training which enables the utilization of large datasets necessary for the three-dimensional flow modeling. Further, we introduce a continuous resampling algorithm that allows to operate on one static dataset. Every feature of our methodology is tested individually and verified against conventional CFD simulations. Finally, we apply our proposed method in context of an exemplary real-world automotive application.