We have re-appraised the temperatures of Red Supergiants (RSGs) in the Magellanic Clouds, by studying their spectral energy distributions (SEDs) from 400–2500 nm using VLT+XSHOOTER, in conjunction with MARCS model atmospheres. We determine temperatures using 3 methods: from model fits to the TiO bands in the optical; from model fits to the SED using the line-free continuum in the near-infrared; and from the integrated fluxes. We find that the temperatures from the TiO fits are systematically lower that those from the other methods by several hundred Kelvin. The TiO fits also dramatically over-predict the flux in the near-IR, and imply extinctions which are anomalously low compared to neighbouring stars. In contrast, the SED temperatures provide good fits to the fluxes at all wavelengths other than the TiO bands, are in agreement with the temperatures from the flux integration method, and imply extinctions consistent with nearby stars. We consider a number of ways to reconcile this discrepancy, concluding that 3-D effects are responsible, and that RSG temperatures are much warmer than previously thought.