This article explores mineral carbonation of municipal solid waste (MSW) incineration bottom ash as a CO2 sequestration method. A mathematical model simulates the carbonation process, optimizing conditions to maximize CO2 capture while minimizing energy and costs. The model incorporates experimental data to accurately predict carbonation rates across varying temperatures and pressures, critical for industrial applications. The model, calibrated and validated using experimental data, demonstrates a high carbonation rate of 75.36 (arbitrary units) at 70 °C and 2.0 atmospheres. However, the study emphasizes energy efficiency. Simulations identify a balance: an efficient rate of 49.59 (arbitrary units) at 0 °C and 1 atmosphere. Further analysis highlights an optimal operating point around 43 °C and 1 atmosphere, balancing efficiency with lower energy demands. These results suggest a promising pathway for greenhouse gas mitigation and waste valorization, demonstrating the influence of temperature and pressure on carbonation.