An analytical inverse heat transfer solution is given for calculating surface heat flux from temperature sensitive coating measurements on a base with a finite thickness, which is particularly relevant to high enthalpy hypersonic wind tunnel experiments. This solution is validated through simulations for several time histories of the heat flux imposed on the surface of the base, focusing on the effects of the relevant parameters including the control parameter in the inverse Laplace transform, base thickness and convective heat transfer on the backside of the base. Further, this solution is used to extract the heat-flux fields from temperature-sensitive-paint images obtained on a flat surface of an aluminum base in a transonic obliquely impinging jet. The experimental data exhibit the self-similar evolution of the surface temperature and heat-flux fields. The Nusselt number distribution evaluated by using this analytical method is consistent with the previous results. (C) 2017 Elsevier Ltd. All rights reserved.