The paradox of the floating candle that continues to burn

What happens after lighting a paraffin candle that is barely floating in water and kept upright with the aid of an appropriately weighted nail attached to its bottom? Presumably, it should sink because the buoyant force will decrease more than the weight. Surprisingly, the candle will continue to burn, rising slowly above the surface of the water. The reason for this is that the flame forms a well around the wick filled with molten paraffin, while the water keeps the outer walls of the candle cool and unscathed. Thus, the buoyancy hardly changes while the weight is reduced through burning, resulting in a floating candle that will rise above water. We present a quantitative model that describes the formation of the well and verify it experimentally, examining first the case of a candle in the air and then the case of a candle immersed in water.