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We present the results of a medium resolution optical spectroscopic survey of92 cool ($3,000 \lesssim T_{\rm eff} \lesssim 4,500\,$K) southern TESScandidate planet hosts, and describe our spectral fitting methodology used torecover stellar parameters. We quantify model deficiencies at predictingoptical fluxes, and while our technique works well for $T_{\rm eff}$, furtherimprovements are needed for [Fe/H]. To this end, we developed an updatedphotometric [Fe/H] calibration for isolated main sequence stars built upon acalibration sample of 69 cool dwarfs in binary systems, precise to$\pm0.19\,$dex, from super-solar to metal poor, over $1.51 < {\rmGaia}~(B_P-R_P) < 3.3$. Our fitted $T_{\rm eff}$ and $R_\star$ have medianprecisions of 0.8% and 1.7%, respectively and are consistent with our sample ofstandard stars. We use these to model the transit light curves and determineexoplanet radii for 100 candidate planets to 3.5% precision and see evidencethat the planet-radius gap is also present for cool dwarfs. Our results areconsistent with the sample of confirmed TESS planets, with this surveyrepresenting one of the largest uniform analyses of cool TESS candidate planethosts to date.

Characterisation of 92 Southern TESS Candidate Planet Hosts and a New Photometric [Fe/H] Relation for Cool Dwarfs