Abstract We present a self-consistent study of cool supergiants (CSGs) belonging to the Magellanic clouds. We calculated stellar atmospheric parameters using LTE KURUCZ and MARCS atmospheric models for more than 400 individual targets by fitting a careful selection of weak metallic lines. We explore the existence of a Teff scale and its implications in two different metallicity environments (each Magellanic cloud). Critical and in-depth tests have been performed to assess the reliability of our stellar parameters (i.e. internal error budget, NLTE systematics). In addition, several Monte Carlo tests have been carried out to infer the significance of the Teff scale found. Our findings point towards a unique Teff scale that seems to be independent of the environment.