Fracture dissolution in the early stages of karstification under hypogene conditions is investigated using a coupled numerical model of fluid flow, heat transfer, and reactive transport. Dissolution of calcite in the H2O-CO2-CaCO3 system along a cooling flow path is investigated using both equilibrium and kinetic models. During the very early stages of fracture growth, there is a positive feedback between flow, heat transfer, and dissolution. In this stage the dissolution rate is largely controlled by the retrograde solubility of calcite, and aperture growth is relatively uniform along the fracture length. There is a period of slow continuous increase in the mass flow rate through the fracture, which is followed by an abrupt rapid increase. We refer to the time when this rapid increase occurs as the maturation time. As the flow rate continues to increase after maturation, forced convective effects lead to higher fluid temperatures in the fracture, resulting in a negative feedback that slows the rate of fracture growth. The behavior of aperture growth before the maturation time can be described by a simple ordinary differential equation. The solution of this differential equation provides an estimate of the maturation time, in terms of the initial aperture, hydraulic and thermal gradients, and the change in solubility with temperature. The behavior before maturation in two-dimensional variable aperture fractures is investigated using a simplified model. The maturation time is shown to decrease with the degree of aperture variability due to highly selective growth along preferential flow paths.