Changes in the extent of the polar alpine glaciers within Taylor Valley, Antarctica, are important for understanding past climates and past changes in ice-dammed lakes. Comparison of ground-based photographs, taken over a 20 year period, shows glacier advances of 2-100 m. Over the past ~103 years the climate has warmed. We hypothesize that an increase in average air temperature alone can explain the observed glacier advance through ice softening. We test this hypothesis by using a flowband model that includes a temperature-dependent softness term. Results show that, for a 2˚C warming, a small glacier (50 km2) advances ~25m and the ablation zone thins, consistent with observations. A doubling of snow accumulation would also explain the glacial advance, but predicts ablation-zone thickening, rather than thinning as observed. Problems encountered in modeling glacier flow lead to two intriguing but unresolved issues. First, the current form of the shape factor, which distributes the stress in simple flow models, may need to be revised for polar glaciers. Second, the measured mass-balance gradient in Taylor Valley may be anomalously low, compared to past times, and a larger gradient is required to develop the glacier profiles observed today.