Coupled climate models and recent observational evidence suggest that Arctic sea ice may undergo abrupt periods of loss during the next fifty years. Here, we evaluate how rapid sea ice loss affects terrestrial Arctic climate and ground thermal state in the Community Climate System Model. We find that simulated western Arctic land warming trends during rapid sea ice loss are 3.5 times greater than secular 21st century climate-change trends. The accelerated warming signal penetrates up to 1500 km inland and is apparent throughout most of the year, peaking in autumn. Idealized experiments using the Community Land Model, with improved permafrost dynamics, indicate that an accelerated warming period substantially increases ground heat accumulation. Enhanced heat accumulation leads to rapid degradation of warm permafrost and may increase the vulnerability of colder permafrost to degradation under continued warming. Taken together, these results imply a link between rapid sea ice loss and permafrost health.