Wire arc additive manufacturing (WAAM) is attracting increasing interest for the production of large metallic components due to its high material efficiency and productivity. However, process instability and heat input fluctuations can compromise geometric consistency, process reliability, and compliance with qualification requirements, while also affecting energy consumption and environmental performance. This study investigates the environmental implications of feedback-controlled heat-input regulation in WAAM of Invar 36, with particular emphasis on carbon footprint through life cycle assessment (LCA). In contrast to conventional WAAM control strategies, which typically target bead geometry, the proposed approach regulates thermal input through online adjustment of the contact tip-to-workpiece distance (CTWD). This enables heat-input control while preserving the nominal welding parameters, which is particularly relevant for qualification-oriented manufacturing. By combining layer-wise thin-wall experiments with scale-up to an industrial Invar 36 component, the study shows that closed-loop heat-input control increased deposited mass per layer by up to 33.8%, while reducing specific energy consumption and WAAM-only global warming potential (GWP) by up to 25.4% and 25.6%, respectively. At the component scale, the measured energy demand decreased from 8.17 to 7.65 kWh and the WAAM-only GWP from 13.2 to 12.5 kg CO₂-eq. These findings confirm that heat-input regularisation improves WAAM process efficiency and process-related sustainability. However, because feedstock production dominates the total environmental impact, the full carbon-footprint benefit can only be achieved if geometry- or mass-based feedback prevents unnecessary material over-deposition. The results therefore indicate that closed-loop control provides the greatest environmental advantage under equal deposited-mass conditions.