The secondary air system of a modern gas or steam turbine is configured to satisfy a number of requirements, such as to purge cavities and maintain a sufficient flow of cooling air to key engine components, for a minimum penalty on engine cycle efficiency and specific fuel consumption. Advanced sealing technologies, such as brush seals and leaf seals, are designed to maintain pressures in cavities adjacent to rotating shafts. They offer significant reductions in secondary air parasitic leakage flows over the legacy sealing technology, the labyrinth seal. The leaf seal comprises a series of stacked sheet elements which are inclined relative to the radial direction, offering increased axial rigidity, reduced radial stiffness, and good leakage performance. Investigations into leaf seal mechanical and flow performance have been conducted by previous researchers. However, limited understanding of the thermal behavior of contacting leaf seals under sustained shaft contact has led to the development of an analytical model in this study, which can be used to predict the power split between the leaf and rotor from predicted temperature rises during operation. This enables the effects of seal and rotor thermal growth and, therefore, implications on seal endurance and rotor mechanical integrity to be quantified. Consideration is given to the heat transfer coefficient in the leaf pack. A dimensional analysis of the leaf seal problem using the method of extended dimensions is presented, yielding the expected form of the relationship between seal frictional power generation, leakage mass flow rate, and rotor temperature rise. An analytical model is derived which is in agreement. Using the derived leaf temperature distribution formula, the theoretical leaf tip temperature rise and temperature distributions are computed over a range of mass flow rates and frictional heat values. Experimental data were collected in high-speed tests of a leaf seal prototype using the Engine Seal Test Facility at Oxford University. These data were used to populate the analytical model and collapsed well to confirm the expected linear relationship. In this form, the thermal characteristic can be used with predictions of mass flow rate and frictional power generated to estimate the leaf tip and rotor temperature rise in engine operation.