It has been suggested that changes in the Atlantic Meridional Overturning Circulation (AMOC) can drive sea surface temperature (SST) on monthly time scales (Duchez et al., 2016, https://doi.org/10.1007/s00382-015-2918-1). However, with only 11 years of continuous observations, the validity of this result over longer, or different, time periods is uncertain. In this study, we use a 120 yearlong control simulation from a high‐resolution climate model to test the robustness of the AMOC fingerprints. The model reproduces the observed AMOC seasonal cycle and its variability, and the observed 5‐month lagged AMOC‐SST fingerprints derived from 11 years of data. However, the AMOC‐SST fingerprints are very sensitive to the particular time period considered. In particular, both the Florida current and the upper mid‐ocean transport produce highly inconsistent fingerprints when using time periods shorter than 30 years. Therefore, several decades of RAPID observations will be necessary to determine the real impact of the AMOC on SSTs at monthly time scales.