This study introduces a novel open boundary treatment method for simulating thermal plumes in natural convection, utilizing a combination of the Perfectly Matched Layer (PML) and local one-dimensional inviscid (LODI) methods within a compressible flow solver for Direct Numerical Simulation (DNS). This innovative approach significantly reduces the size of the computational domain yet effectively captures the complex transition from laminar to turbulent flow. Validation of the proposed methodology includes comparisons with existing empirical formulations, experimental data, and well-resolved DNS results, incorporating both time-averaged and spectral analyses. Additionally, the buoyancy-induced laminar-turbulent transition is investigated to enhance understanding of the dynamics and behaviors of thermal plumes. The findings offer insights into optimizing computational efficiency without compromising the accuracy needed to analyze intricate fluid dynamics in thermal engineering applications.