  Intensity-interferometry based on Hanbury-Brown and Twiss's seminal
experiment for determining the radius of the star Sirius formed the basis for
developing the quantum theory of light. To date, the principle of this
experiment is used in various forms across different fields of quantum optics,
imaging and astronomy. Though, the technique is powerful, it has not been
generalized for objects at different temperatures. Here, we address this
problem using a generating functional formalism by employing the P-function
representation of quantum-thermal light. Specifically, we investigate the
photon coincidences of a system of two extended objects at different
temperature using this theoretical framework. We show two unique aspects in the
second-order quantum coherence function - interference oscillations and a
long-baseline asymptotic value that depends on the observation frequency,
temperatures and size of both objects. We apply our approach to the case of
binary stars and discuss the advantages of measuring these two features in an
experiment. In addition to the estimation of the radii of each star and the
distance between them, we also show that the present approach is suitable for
the estimation of temperatures as well. To this end, we apply it to the
practical case of binary stars Luhman 16 and Spica $\alpha$ Vir. We find that
for currently available telescopes, an experimental demonstration is feasible
in the near term. Our work contributes to the fundamental understanding of
intensity interferometry of quantum-thermal light and can be used as a tool for
studying two-body thermal emitters - from binary stars to extended objects.
