We compare high resolution infrared observations of the CO 3-1 bands in the 2.297-2.310 micron region of M dwarfs and one L dwarf with theoretical expectations. We find a good match between the observational and synthetic spectra throughout the 2000-3500K temperature regime investigated. Nonetheless, for the 2500-3500 K temperature range the temperatures that we derive from synthetic spectral fits are higher than expected from more empirical methods by several hundred K. In order to reconcile our findings with the empirical temperature scale it is necessary to invoke warming of the model atmosphere used to construct the synthetic spectra. We consider that the most likely reason for the back-warming is missing high temperature opacity due to water vapour. We compare the water vapour opacity of the Partridge & Schwenke (1997) line list used for the model atmosphere with the output from a preliminary calculation by Barber & Tennyson (2004). While the Partridge & Schwenke line list is a reasonable spectroscopic match for the new line list at 2000 K, by 4000 K it is missing around 25% of the water vapour opacity. We thus consider that the offset between empirical and synthetic temperature scales is explained by the lack of hot water vapour used for computation of the synthetic spectra. For our coolest objects with temperatures below 2500 K we find best fits when using synthetic spectra which include dust emission. Our spectra also allow us to constrain the rotational velocities of our sources, and these velocities are consistent with the broad trend of rotational velocities increasing from M to L.
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