The CLAW postulate states that an increase in solar irradiance or in the heat flux to the ocean can trigger a biogeochemical response to counteract the associated increase in temperature and available sunlight. This natural (negative) feedback mechanism would be based on a multistep response: first, an increase in seawater dimethylsulfide concentrations (DMS_w) and therefore its fluxes to the atmosphere (DMS_flux); second, an increase in the atmospheric cloud condensation nuclei (CCN) burden as a consequence of DMS oxidation to form biogenic CCN (CCN_bio); and third, an increase in cloud albedo due to higher CCN numbers. Monthly global climatological fields of the solar radiation dose in the upper mixed layer (SRD), surface oceanic DMS_w, model outputs of hydroxyl radical concentrations (OH), and satellite‐derived CCN numbers (CCN_s) are analyzed in order to evaluate the proposed “solar radiation dose‐DMS‐CCN” link from a global point of view. OH is included as the main atmospheric oxidant of the estimated DMS_flux to produce CCN_bio. Global maps of seasonal correlations between the variables show that the solar radiation dose is highly (positively) correlated with seawater dimethylsulfide over most of the global ocean and that atmospheric DMS oxidation is highly (positively) correlated with CCN_s over large regions. These couplings are stronger at high latitudes, whereas the regions with negative or no correlation are located at low latitudes around the equator. However, CCN_bio estimates for 15 regions of the global ocean show that DMS oxidation can be an important contributor to the CCN_s burden only over pollution‐free regions, while it would have a minor contribution over regions with high loads of continental aerosols. Globally, the mean annual contribution of CCN_bio to total CCN_s is estimated to be ≈30%. Our results support that an oceanic biogenic mechanism that modulates cloud formation and albedo can indeed occur, although its impact seems rather weak over regions under a strong influence of continental aerosols. Nevertheless, our approach does not fully rule out that the observed correlations are due to an independent seasonal variation of the studied variables; seasonal couplings are necessary but not sufficient conditions to prove the CLAW hypothesis.