Here, we study B20-type RhGe, a representative of a class of non-centrosymmetric monosilicides and monogermanides, which possess unique topological and magnetic properties important for many possible applications. The stability and phase transitions of the non-equilibrium B20-RhGe phase that can only be obtained under high pressure, are investigated theoretically using ab initio calculations and experimentally by means of dierential scanning calorimetry. For RhGe and, for comparison, for its analogue RhSi, we conducted an evolutionary search for low-energy polymorphic modications at zero temperature and then performed simulations of their behavior at nite temperatures. The (P; T) conditions of stability for the found polymorphs are determined. Our calorimetric studies on high-pressure-synthesized RhGe samples allowed us to reveal peculiarities in thermal stability and heating-induced phase transformations. X-ray diffraction analysis and microstructure analysis of the samples were carried out before and after the heating. We also determined the specic heat from calorimetric measurements and compared the results with our calculations in the quasi-harmonic approximation.