Earth system models (ESMs) generally project an increase in Southern Ocean net primary production (NPP) under future warming, whereas the NPP satellite product shows a decreasing trend. Part of this discrepancy may arise from the direct temperature dependence embedded in phytoplankton growth formulations, which increases simulated NPP as the ocean warms. Here we introduce temperature-normalised NPP (TNNPP), a diagnostic that removes the model-specific direct temperature-growth contribution from simulated NPP. Using Coupled Model Intercomparison Project Phase 6 (CMIP6) ESMs, we compare historical NPP and TNNPP with CbPM-derived satellite NPP over 1998-2025 and examine future changes under the SSP2-4.5 scenario. TNNPP reduces the magnitude mismatch with CbPM and slightly improves the agreement in trend sign. Box-model experiments show that the NPP-TNNPP difference primarily reflects the removed temperature-growth contribution, while the residual TNNPP response reflects other simulated biogeochemical and environmental changes. In future projections, conventional NPP increases over much of the Southern Ocean, whereas TNNPP declines substantially by 2100. The residual TNNPP response is associated with nutrient-related variability in the open ocean zone and with light availability in the sea-ice zone. These results indicate that the projected increase in Southern Ocean NPP includes a substantial temperature-growth contribution. TNNPP removes this NPP-temperature coupling, making it useful as an additional diagnostic for interpreting productivity responses under climate warming.