Rockwall permafrost is increasingly investigated because of its possible role in bedrock failure, related hazards and geotechnical practices. In this study, we simulate the possible permafrost pathways during the 21 st century of one of the coldest rock ridge in the European Alps: the Grand Pilier d'Angle (4305 m a.s.l). Rockwalls permafrost evolution is primarily driven by air temperature and we thus run simulations with 13 climate models declined with the most contrasted greenhouse gas emissions scenarios (RCP2.6 and 8.5) until 2100 to account for climate models uncertainty. Results show that by 2050 permafrost would have warmed by about 1°C down to 35 m depth compared to 2020, and that about 50, and 30 % of this perturbation will reach depths of 80 and 130 m respectively. But uncertainty remains rather high before mid-century and possible permafrost pathways are more reliable after 2050. By the end of the century, a "business as usual" scenario would result in a surge in permafrost degradation with +3 ±1.3 and +1.4 ±0.6 °C at 35 m and 130 m depth respectively. In narrow topographies where heat fluxes from opposite faces merge such as the top of our study site, the temperature increase would be enhanced, reaching +4°C ±1.9°C. In this scenario, permafrost would thaw in most alpine rockwalls except shaded rock faces > 4000 m a.s.l. that are several tens to hundreds of meters apart from sun-exposed faces such as the north face of our study site. Conversely, drastic reduction in greenhouse gas emissions would result in a stabilization in permafrost degradation, restricting bedrock thawing to sun-exposed and shaded faces below 4000 and 3000 m a.s.l. respectively, where warm permafrost is currently present.