This research develops a conceptual model of a karst system subject to mountain permafrost. The transient thermal response of a frozen rock cleft after the rise in the atmospheric temperature above the melting temperature of water is investigated using numerical simulations. Free convection in liquid water (i.e. buoyancy-driven flow) is considered. The density increase in water from 0 to 4 °C causes warmer meltwater to flow downwards and colder upwards, resulting in significant enhancement of the heat transferred from the ground surface to the melting front. Free convection increases the melting rate by approximately an order of magnitude compared to a model based on thermal conduction in stagnant water. The model outcomes are compared qualitatively with field data from the Monlesi ice cave (Switzerland) and confirm the agreement between real-world observations and the proposed model when free convection is considered.