Ice caps that are mostly frozen at the bedrock-ice interface are thought to be stable and respond slowly to changes in climate. We use remote sensing to measure velocity and thickness changes that occur when the margin of the largely cold-based Vavilov Ice Cap in the Russian High Arctic advances over weak marine sediments. We show that cold-based to polythermal glacier systems with no previous history of surging may evolve with unexpected and unprecedented speed when their basal boundary conditions change, resulting in very large dynamic ice mass losses (an increase in annual mass loss by a factor of ∼100) over a few years. We question the future long-term stability of cold and polythermal polar ice caps, many of which terminate in marine waters as the climate becomes warmer and wetter in the polar regions.