High-resolution, near-infrared spectra will be the primary tool for finding and characterizing Earth-like planets around low-mass stars. Yet, the properties of exoplanets cannot be precisely determined without accurate and precise measurements of the host star. Spectra obtained with the Immersion Grating Infrared Spectrometer simultaneously provide diagnostics for most stellar parameters, but the first step in any analysis is the determination of the effective temperature. Here we report the calibration of high-resolution H-band spectra to accurately determine the effective temperature for stars between 4000 and 3000K (~K8-M5) using absorption line-depths of FeI, OH, and Al I. The field star sample used here contains 254 K and M stars with temperatures derived using BT-Settl synthetic spectra. We use 106 stars with precise temperatures in the literature to calibrate our method, with typical errors of about 140K, and systematic uncertainties less than ~120K. For the broadest applicability, we present Teff-line-depth-ratio relationships, which we test on 12 members of the TW Hydrae Association and at spectral resolving powers between ~10000 and 120000. These ratios offer a simple but accurate measure of effective temperatures in cool stars that are distance and reddening independent.