To improve the design process of geothermal systems, it is important to know which design parameters particularly affect the performance of the system. This article presents investigations on design parameters for borehole heat exchangers in the shallow subsurface. The study is based on numerical simulations with one double U-tube borehole heat exchanger and approximated models obtained using machine learning. As a result of the global sensitivity analysis, relevant parameters are identified and their respective influence on the performance of a borehole heat exchanger is compared. For example, according to this analysis, the three parameters with the highest sensitivity are the initial temperature, the heat demand and the share of the borehole heat exchanger that is surrounded by groundwater flow. Finally, the effects of uncertainties in the parameters identified as relevant for the design of a borehole heat exchanger are considered in an uncertainty quantification for a fictitious site. Uncertainties for regulatory compliance with respect to temperature limits as well as a large probability of oversizing the system were identified for the considered example. The results of the exemplary uncertainty quantification indicate that it has the potential to be a useful tool for planning practice.