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We compare mid-infrared 3.6 and 4.5 $\mu$m Warm Spitzer observations forCepheids in the Milky Way and the Large and Small Magellanic Clouds. Usingmodels, we explore in detail the effect of the CO rotation-vibration band-headat 4.6 $\mu$m on the mid-infrared photometry. We confirm the temperaturesensitivity of the CO band-head at 4.6 $\mu$m and find no evidence for aneffect at 3.6 $\mu$m. We compare the ([3.6]-[4.5]) period-colour relations inthe MW, LMC, and SMC. The slopes of the period-colour relations for the threegalaxies are in good agreement, but there is a trend in zero-point withmetallicity, with the lowest metallicity Cepheids having redder mid-IR colours.Finally, we present a colour-[Fe/H] relation based on published spectroscopicmetallicities. This empirical relation, calibrated to the metallicity system ofGenovali et al. (2014), demonstrates that the ([3.6]-[4.5]) colour provides areliable metallicity indicator for Cepheids, with a precision comparable tocurrent spectroscopic determinations.

The Carnegie Chicago Hubble Program: The Mid-Infrared Colours of Cepheids and the Effect of Metallicity on the CO Band-head at $4.6\mu$m