  The NASA K2 mission uses photometry to find planets transiting stars of
various types. M dwarfs are of high interest since they host more short period
planets than any other type of main sequence stars and transiting planets
around M dwarfs have deeper transits compared to other main sequence stars. In
this paper, we present stellar parameters from K and M dwarfs hosting
transiting planet candidates discovered by our team. Using the SOFI
spectrograph on the European Southern Observatory's New Technology Telescope,
we obtained R ~ 1000 J-, H-, and K-band (0.95 - 2.52 microns) spectra of 34
late-type K2 planet and candidate planet host systems and 12 bright K4-M5
dwarfs with interferometrically measured radii and effective temperatures. Out
of our 34 late-type K2 targets, we identify 27 of these stars as M dwarfs. We
measure equivalent widths of spectral features, derive calibration relations
using stars with interferometric measurements, and estimate stellar radii,
effective temperatures, masses, and luminosities for the K2 planet hosts. Our
calibrations provide radii and temperatures with median uncertainties of 0.059
R_sun (16.09%) and 160 K (4.33%), respectively. We then reassess the radii and
equilibrium temperatures of known and candidate planets based on our
spectroscopically derived stellar parameters. Since a planet's radius and
equilibrium temperature depends on the parameters of its host star, our study
provides more precise planetary parameters for planets and candidates orbiting
late-type stars observed with K2. We find a median planet radius and an
equilibrium temperature of approximately 3R_earth and 500 K, with several
systems (K2-18b and K2-72e) receiving near-Earth like levels of incident
irradiation.
