The societal importance of geothermal energy is significantly increasing because of its low carbon-dioxide footprint. However, geothermal exploration is also subject to high risks. For a better assessment of these risks, extensiveparameter studies are required that improve our understanding of the subsurface. This yields computationally demanding analyses. Often this is compensated by constructing models with a low vertical extent. In this paper, we demonstrate that this leads to entirely boundary-dominated and hence uninformative models. We demonstrate the indispensable requirement to construct models with a large vertical extent to obtain informative models with respect to the model parameters. For this quantitative investigation, global sensitivity studies are essential since they also consider parameter correlations. To compensate for the computationally demanding nature of the analyses, we employ a physics-based machine learning approach, namely the reduced basis method, instead of reducing the physical dimensionality of the model. The reduced basis method yields a significant cost reduction while preserving the physics and a high accuracy, thus providing a more efficient alternative to considering, for instance, a lower vertical extent. The reduction of the mathematical instead of physical space leads to less restrictive models and, hence, maintains the model prediction capabilities. We use this combination of methods for a detailed investigation of the influence of model boundary settings in typical regional-scale geothermal simulations and highlight potential problems.