Glacier deposits are used to reconstruct past climate, but the same glacier size can result from different mixes of temperature and snowfall. Using numerical glacier simulations in the Bolivian Andes, we explored how to overcome this ambiguity. We show that combining several neighboring glaciers with independent rainfall records partly resolves it, giving temperatures 0.8°C and 1.3°C lower during the Little Ice Age and Early Holocene (~10,000 years ago), respectively.