The processes involved in the formation and storage of magma within the Earth's upper crust are of fundamental importance to volcanology. Many volcanic eruptions, including some of the largest, result from the eruption of components stored for tens to hundreds of thousands of years before eruption(1-3). Although the physical conditions of magma storage and remobilization are of paramount importance for understanding volcanic processes, they remain relatively poorly known(4,5). Eruptions of crystal-rich magma are often suggested to require the mobilization of magma stored at near-solidus conditions(6-8); however, accumulation of significant eruptible magma volumes has also been argued to require extended storage of magma at higher temperatures(7-9). What has been lacking in this debate is clear observational evidence linking the thermal (and therefore physical) conditions within a magma reservoir to timescales of storage-that is, thermal histories. Here we present a method of constraining such thermal histories by combining timescales derived from uranium-series disequilibria, crystal sizes and trace-element zoning in crystals. At Mount Hood (Oregon, USA), only a small fraction of the total magma storage duration (at most 12 per cent and probably much less than 1 per cent) has been spent at temperatures above the critical crystallinity (40-50 per cent) at which magma is easily mobilized. Partial data sets for other volcanoes also suggest that similar conditions of magma storage are widespread and therefore that rapid mobilization of magmas stored at near-solidus temperatures is common. Magma storage at low temperatures indicates that, although thermobarometry calculations based on mineral compositions may record the conditions of crystallization, they are unlikely to reflect the conditions of most of the time that the magma is stored. Our results also suggest that largely liquid magma bodies that can be imaged geophysically will be ephemeral features and therefore their detection could indicate imminent eruption.