Coronal cavities are large low-density regions formed by hemispheric-scale magnetic flux ropes suspended in the Sun's outer atmosphere. They evolve over time, eventually erupting as the dark cores of coronal mass ejections. Although coronal mass ejections are common and can significantly affect planetary magnetospheres, the mechanisms by which cavities evolve to an eruptive state remain poorly understood. Recent optical observations of high-latitude 'polar crown' prominences within coronal cavities reveal dark, low-density 'bubbles' that undergo Rayleigh-Taylor instabilities to form dark plumes rising into overlying coronal cavities. These observations offered a possible mechanism for coronal cavity evolution, although the nature of the bubbles, particularly their buoyancy, was hitherto unclear. Here we report simultaneous optical and extreme-ultraviolet observations of polar crown prominences that show that these bubbles contain plasma at temperatures in the range (2.5-12) × 10(5) kelvin, which is 25-120 times hotter than the overlying prominence. This identifies a source of the buoyancy, and suggests that the coronal cavity-prominence system supports a novel form of magneto-thermal convection in the solar atmosphere, challenging current hydromagnetic concepts of prominences and their relation to coronal cavities.