The problem of deducing the temperature profile of a weakly inhomogeneous, incoherent radiating object from external field measurements is addressed within the framework of classical second-order scalar coherence theory. Within this framework it is shown that the problem can be cast into an inverse radiometric problem using the concepts of generalized radiometry first introduced by Adrian Walther and subsequently extended and developed by Emil Wolf. The inverse radiometric problem is shown to be solvable by the reconstruction algorithms of diffraction tomography. Diffraction tomography is the generalization of conventional (x-ray) tomography to applications where wave (propagation) effects are dominant. In the usual applications of diffraction tomography an object is illuminated by an external wave and the resulting scattered wave is measured. In the problem under consideration here the object is not illuminated by an external wave. Rather the measured wave is emitted as a result of the temperature profile of the object. For this reason we have called the method propagation emission tomography. The presentation includes computer simulations of propagation emission tomography together with a discussion of practical applications of the method.