Advance and retreat of temperate glaciers is largely controlled by changes in temperature and precipitation, but the relative importance of these drivers is debated. Numerical modeling of a New Zealand glacier reveals that temperature is the dominant control on glacier length. We find that a glacial advance, dated to ca. 13,000 yr B.P., requires a cooling event of 3–4 °C. This mid-latitude Southern Hemisphere cooling is similar in magnitude to the Antarctic Cold Reversal in the Vostok ice core record and likely to be a response to the same climate signal.