This work investigates steady-state thermal blooming of a high-energy laser in the presence of laser-driven convection. While thermal blooming has historically been simulated with prescribed fluid velocities, the model introduced here solves for the fluid dynamics along the propagation path using a Boussinesq approximation to the incompressible Navier-Stokes equations. The resultant temperature fluctuations were coupled to refractive index fluctuations, and the beam propagation was modeled using the paraxial wave equation. Fixed-point methods were used to solve the fluid equations as well as to couple the beam propagation to the steady-state flow. The simulated results are discussed relative to recent experimental thermal blooming results [Opt. Laser Technol.146, 107568 (2022) OLTCAS0030-399210.1016/j.optlastec.2021.107568], with half-moon irradiance patterns matching for a laser wavelength at moderate absorption. Higher energy lasers were simulated within an atmospheric transmission window, with the laser irradiance exhibiting crescent profiles.