Resistance to groundwater flow and temperature-dependent solubility of calcite is affected by the flow-induced heat convection in groundwater flow systems, which impacts the dissolution of limestone. The primary objective of this paper is to quantify the effect of convective heat transport in modelling the early evolution of conduits, using a flow-heat-solute coupled karst evolution model. The results show that the enlargement of conduits induced by convective heat transport occurs mainly in a region with a decreased temperature and a increased flux of water. For the initial homogeneous aquifer with conduits that had a diameter of 1E-5 m (Scenario 1), convective heat transport accelerated the karstification progress by 2.5% (3640 years out of 147470 years) and enlarged the diameter of the evolved cave beneath the water table. For the initially heterogeneous model, which was cut by a steeply dipping fault (Scenario 2), heat convection prolonged the early evolution of conduits by 110 years and pushed the proto-conduit along the fault down by approximately 150 m. The maximum diameter of the proto-conduit was reduced, but the total number of dissolved conduits increased. With an increase in the geothermal gradient by 20 degrees C/km in the heterogeneous model (Scenario 3), the lag-time caused by the convective heat transport increased to 6830 years, and the depth of the proto-conduit increased by 450 m. Although a delay of thousands of years is negligible for the karstification process over millions of years, differences in diameter and depth of karst formation provide some quantitative guidelines for when conduit evolution may be simulated by assuming a constant or depth-dependent temperature as a reasonable compromise between accuracy and efficiency.