Shock wave interactions such as those that occur during atmospheric re-entry, can produce extreme thermal loads on aerospace structures. These interactions are reproduced experimentally in hypersonic wind tunnels to study how the flow structures relate to the deleterious heat fluxes. In these studies, localized fluid jets created by shock interactions impinge on a test cylinder, where the temperature due to the heat flux is measured. These measurements are used to estimate the heat flux on the surface as a result of the shock interactions. The nature of the incident flux usually involves dynamic transients and severe nonuniformities. Finding this boundary flux from discrete unsteady temperature measurements is characterized by instabilities in the solution. The purpose of this work is to evaluate existing methodologies for the determination of the unsteady heat flux and to introduce a new approach based on an inverse technique. The performance of these methods was measured first in terms of accuracy and their ability to handle inherently ``unstable'' or highly dynamic data such as step fluxes and high frequency oscillating fluxes. Then the method was expanded to estimate unsteady and nonuniform heat fluxes. The inverse methods proved to be the most accurate and stable of the methods examined, with the proposed method being preferable.