We have applied the InfraRed Flux Method (IRFM) to a sample of approximately 500 giant stars in order to derive their effective temperatures with an internal mean accuracy of about 1.5% and a maximum uncertainty in the zero point of the order of 0.9%. For the application of the IRFM, we have used a homogeneous grid of theoretical model atmosphere flux distributions developed by cite[Kurucz (1993)]{K93}. The atmospheric parameters of the stars roughly cover the ranges: 3500 K <= T_eff <= 8000 K; -3.0 <= [Fe/H] <= +0.5; 0.5 <= log (g) <= 3.5. The monochromatic infrared fluxes at the continuum are based on recent photometry with errors that satisfy the accuracy requirements of the work. We have derived the bolometric correction of giant stars by using a new calibration which takes the effect of metallicity into account. Direct spectroscopic determinations of metallicity have been adopted where available, although estimates based on photometric calibrations have been considered for some stars lacking spectroscopic ones. The adopted infrared absolute flux calibration, based on direct optical measurements of stellar angular diameters, puts the effective temperatures determined in this work in the same scale as those obtained by direct methods. We have derived up to four temperatures, TJ, TH, TK and T_{L'}, for each star using the monochromatic fluxes at different infrared wavelengths in the photometric bands J, H, K and L'. They show good consistency over 4000 K, and there is no appreciable trend with wavelength, metallicity and/or temperature. We provide a detailed description of the steps followed for the application of the IRFM, as well as the sources of error and their effect on final temperatures. We also provide a comparison of the results with previous work.