Hyperspectral images are made up of energy measurements at different wavelengths of light. The case is considered where these measurements are dependent on temperature, the self-emitted energy (emissivity), and reflected energy (downwelling radiance) from the surroundings. The process where the downwelling radiance is fixed and the temperature and emissivity are estimated is referred to as temperature/emissivity separation. Due to the way these terms mix, for a given set of measurements, there exist many pairs of temperatures and emissivities that satisfy the model. This creates ambiguity in the solution that must be resolved for the result to have any significance. A new model is developed which reduces this ambiguity. This model is used to form an objective function. The temperature and emissivity which maximize the value of the objective function are solved for given a set of measurements. As part of the solution, a new algorithm is developed which exploits the shape of the objective function to estimate the temperature and emissivity quickly and accurately. Extensive testing of this algorithm is performed to gain an understanding of its average speed and accuracy.