A solution method is proposed to the inverse problem of determining the unknown initial temperature distribution in a laser-exposed test material from measurements provided by infrared radiometry. A Fredholm integral equation of the first kind is derived that relates the temporal evolution of the infrared signal amplitude to the unknown initial temperature distribution in the exposed test material. The singular-value decomposition is used to demonstrate the severely ill-posed nature of the derived inverse problem. Three inversion methods are used to estimate solutions for the initial temperature distribution. A nonnegatively constrained conjugate-gradient algorithm using early termination is found superior to unconstrained inversion methods and is applied to image the depth of laser-heated chromophores in human skin.