Using an in situ lunar regolith as a construction material in combination with 3D printing not only reduces the weight of materials carried from the Earth but also improves the automation of lunar infrastructure construction. This study aims to improve the printability of a geopolymer based on a BH-1 lunar regolith simulant, including the extrudability, open time, and buildability, by controlling the temperature and adding admixtures. Rheological parameters were used to represent printability with different water-to-binder ratios, printing temperatures, and contents of additives. The mechanical properties of the hardening geopolymer with different filling paths and loading directions were tested. The results show that heating the printed filaments with a water-to-binder ratio of 0.32 at 80 °C can adjust the printability without adding any additive, which can reduce the construction cost of lunar infrastructure. The printability of the BH-1 geopolymer can also be improved by adding 0.3% Attagel-50 and 0.5% polypropylene fiber by mass at a temperature of 20 °C to cope with the changeable environmental conditions on the Moon. After curing under a simulated lunar environment, the 72-h flexural and compressive strengths of the geopolymer specimens reach 4.1 and 48.1 MPa, respectively, which are promising considering that the acceleration of gravity on the Moon is 1/6 of that on the Earth.