Some CMIP6 models show a strong temperature increase in response to greenhouse gases, seemingly inconsistent with past observations. This study investigates this discrepancy using the IPSL-CM6A-LR model and finds that members with lower warming rates over the past 6-7 decades also exhibit a significant internally-driven AMOC weakening. This matches observational AMOC fingerprints, suggesting internal variability dampened historical warming. Accounting for this AMOC weakening increases the risk of exceeding the 2°C warming threshold.