Unsteady transport of energy in a single rock fracture is studied here. The fracture is modelled as closely spaced parallel plates with a distribution of circular contact areas. The thermal problem arises from a sudden increase in inflow temperature. The rate at which the bulk of the fluid in the fracture is heated has been determined in this study using a finite element method. Results show that bulk heating of the fluid is independent of the presence of contact areas at low Peclet numbers (Pe < 1). For large Peclet numbers (Pe > 10), a thermal front moves through the fracture. The front velocity increases proportionally with increasing contact area.