  The temperatures of red supergiants (RSGs) are expected to depend on
metallicity (Z) in such a way that lower-Z RSGs are warmer. In this work, we
investigate the Z-dependence of the Hayashi limit by analysing RSGs in the
low-Z galaxy Wolf-Lundmark-Mellote (WLM), and compare with the RSGs in the
higher-Z environments of the Small Magellanic Cloud (SMC) and Large Magellanic
Cloud (LMC). We determine the effective temperature ($T_{\textrm{eff}}$) of
each star by fitting their spectral energy distributions, as observed by
VLT+SHOOTER, with MARCS model atmospheres. We find average temperatures of
$T_{\textrm{eff}_{\textrm{WLM}}}=4400\pm202$ K,
$T_{\textrm{eff}_{\textrm{SMC}}}=4130\pm103$ K, and
$T_{\textrm{eff}_{\textrm{LMC}}}=4140\pm148$ K. From population synthesis
analysis, we find that although the Geneva evolutionary models reproduce this
trend qualitatively, the RSGs in these models are systematically too cool. We
speculate that our results can be explained by the inapplicability of the
standard solar mixing length to RSGs.
