Recently, we proposed an active thermal extraction (ATX) scheme that enables thermally populated surface phonon polaritons to escape into the far-field. The concept is based on a fluorescence upconversion process that also occurs in laser cooling of solids (LCS). Here, we present a generalized analysis of our scheme using the theoretical framework for LCS. We show that both LCS and ATX can be described with the same mathematical formalism by replacing the electron-phonon coupling parameter in LCS with the electron-photon coupling parameter in ATX. Using this framework, we compare the ideal efficiency and power extracted for the two schemes and examine the parasitic loss mechanisms. This work advances the application of ATX to manipulate near-field thermal radiation for applications such as temperature sensing and active radiative cooling.