Spectral lines with high and low excitation potentials respond differently to changes of the effective temperature (T eff), making the ratio of their depths (or equivalent widths) a very sensitive temperature indicator. We derive a set of 100 equations relating T eff to the line-depth ratios, calibrated against accurate (to within 1%) published temperature determinations for giants. These relations are used to determine very accurate temperatures for a sample of 110 giants with nearly solar metallicities based on high-resolution (R = 42 000) échelle spectra with high signal-to-noise ratios (SNRs). The calibration relations are valid for temperatures of 4000–7000 K (F2III–K4III). The internal errors of each of the calibration relations are below 95 K, and applying all these relations together to spectra with SNR = 100 reduces the errors to 5–25 K (1 ?). A major advantage of this technique is that it is independent from interstellar reddening, spectroscopic resolution, and line broadening due to rotation and microturbulence.