To reduce CO${}_2$ emissions in the industrial sector, high-temperature heat pumps are a key technology. This work presents an approach to design such an industrial heat pump system capable of supplying 200 ${}^{°}$C sink temperature and a capacity of approximately 1 MW. Today’s market-available heat pumps using displacement compressors are not suitable for reaching that high sink temperatures as they need lubricating oil, which is not temperature resistant enough. As a consequence, in this study a transcritical heat pump cycle using a two-stage oil-free radial compressor is investigated. Based on preliminary studies, R1233zd(E) is chosen as a refrigerant. The procedure couples 1D thermodynamic cycle simulations with a radial compressor mean-line design model. A preliminary geometry for a compressor with and without inlet guide vanes is presented, and compressor maps including the compressors behaviour in off-design are calculated. The compressor design is then imported into a 1D simulation to analysis the performance of the heat pump in the whole operating range. In the analysis, the application of a fixed inlet is evaluated, and an improvement of approximately 21% and 16% of the isentropic efficiency is achieved. The thermodynamic simulations showed a maximum COP of approximately 2.8 and a possible operating range of 0.5 to 1.3 MW thermal power. Furthermore, a techno-economical analysis by means of a deep-fryer use case showed reasonable payback times of between 2 and 10 years, depending on the electricity to gas price ratio.