We report on the verification of the multiple scattering and thermal emission model PILOT-EX described in a previous publication and extend the scope to include non-isothermal clouds. We also verify the expressions leading to the thermal version of the radiative transfer equation, fill in the details of the Gaussian spherical cloud formulation, describe methods for treating the emissivity correction for limited bandpass instruments, and discuss the significance of the results in terms of radiation contrast and aerosol-induced noise. We extend the model to include arbitrary "embedded sources" and verify results against standards in the literature over a variety of incident angles and demonstrate the significance of the results in computing infrared contrast for use in imaging systems performance analysis. A major finding is that comparisons with known (isothermal) solutions show agreement to within five significant figures for the case of plane layers for both normal incidence and various slant path angles. Also, preliminary results for the case of temperature stratification demonstrate a significant build up of radiance in the (hotter) cloud interior, which leads to lower values of the apparent emissivity for non-isothermal clouds.