Radial-Inflow Turbines are considered the most suited expanders for waste heat recovery via high-temperature mini-organic Rankine Cycle (ORC) turbogenerators thanks to high compactness, large expansion ratio handled by a single stage, and comparatively low weight. Reaching high efficiency in these machines is however a formidable challenge, as they are bounded to operate with expansion ratios exceeding 40. Although scarcely investigated in the published literature, the size of the stator-rotor radial gap is a key design parameter as it has a large influence on fluid-dynamic performance, manufacturing, and mechanical integrity. In addition, the working conditions of the turbine are such that the stator operates with highly supersonic flows in the non-ideal thermodynamic regime, making the flow pattern in stator-rotor radial gap, which can be regarded as an area-decreasing channel, very complex. Under these conditions, the radial gap size could impact the stage efficiency up to few percentage points. The paper presents a study aimed at investigating the impact of variable radial gap on the fluid-dynamic performance of radial-inflow turbines for high-temperature mini-ORC power systems. The reference turbine is a supersonic machine for laboratory experiments under realization at Delft University of Technology, referred to as ORCHID turbine. First, a theoretical analysis is carried out to identify the relevant non-dimensional parameters governing the flow physics in the gap. Then, the effect of the radial gap size on the fluid-dynamic performance of the ORCHID turbine is assessed by means of RANS and uRANS computations. The results show that the change in radial gap size leads to a redistribution of expansion ratio between vaned and vaneless part of stationary component via a substantial change of the stator trailing edge flow structures, which, in turn strongly affects stator loss and stage efficiency, leading to 8% points reduction.