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Construction 3D Printing (C3DP) with sulfur concrete holds great potential for sustainable construction on Earth and beyond. However, a key challenge is optimizing the thermal C3DP process to minimize layer deformations while enhancing interlayer adhesion for improved mechanical strength. To tackle this challenge, this paper presents a physics-based model of heat transfer within a 3D-printed sulfur concrete structure. Numerical implementations of the model are proposed for 3D and 2D structures in Cartesian coordinates. Upon calibration, the model estimates the spatiotemporal distribution of the temperature within the structure based on thermal properties, printing parameters, and environmental conditions. The model is calibrated using experimental data, where the effect of printing parameters is analyzed, and is then utilized to simulate multiple terrestrial and Martian construction scenarios. It identifies a range of printing speeds and interlayer delays that optimize extrudate properties, while also enabling automated control of the thermal C3DP process for optimal performance.