1 Introduction

The scale of temperatures of giant stars has been the target of a number of previous studies based on both direct and indirect methods (e.g. Ridgway et al. 1980; Bell & Gustafsson 1989; Blackwell et al. 1990; Mozurkewich et al. 1991; Richichi et al. 1992; Di Benedetto 1993, 1998; Dyck et al. 1998). In spite of these substantial efforts, very little attention has been paid to the role played by metallicity, especially in the case of direct methods given the restrictions on their application. Nevertheless, metallicity may have a non-negligible influence when applying the effective temperature scale to the analysis of important problems in astrophysics, such as the determination of chemical abundances from spectroscopy, the colour synthesis of stellar populations, the correct interpretation of the observed HR diagram and the observational test of stellar fluxes generated with atmospheric models.

The direct methods for measuring stellar angular diameters (i.e. mainly Michelson interferometry at different wavelengths and lunar occultation measurements) establish the empirical effective temperature scale of Population I giants ([Fe/H] $\sim$ 0) from G0III to M8III. Even in this case, on the observational side the error sources affecting the processes of measurement and reduction of the data make it difficult to ascertain such basic questions as whether spherical effects in the extended atmopsheres of the cooler stars are relevant. On the theoretical side the application of the limb-darkening correction remains unsure. This entails uncertainties concerning the nature of the stellar atmospheres in the range of late spectral types and low surface gravities. The present status for metal-poor giant stars is still more uncertain, given that no interferometric measurements of stellar diameters are available over the whole range of temperatures. A number of indirect methods based on stellar atmosphere models may be applied to determine the effective temperatures of giant stars (see for instance the review by Böhm-Vitense 1981). Unfortunately, theoretically based temperatures are not as trustworthy as would be desirable since atmosphere models cannot reproduce the observed fluxes with the required accuracy, especially in the UV range (e.g. Morossi et al. 1993). The suspicion that these problems are related to the adopted metal line opacities--a probable excess opacity for giants (Malagnini et al. 1992)--makes the temperature scale of metal-deficient stars more uncertain. In addition to their partial dependence on models, most of the previous works concerning the $T_{\rm eff}$ scale for metal-deficient giants have the additional drawback of the low number of stars. As a consequence, the uncertainties in the calibration of $T_{\rm eff}$ versus colour and metallicity are larger than desirable.

In order to overcome the above mentioned disadvantages, we have carried out a programme aimed at a more reliable definition of the effective temperature scale of giant stars (F0-K5). This work is part of a long term programme aimed at a complete revision of the $T_{\rm eff}$ scale of the different regions of the HR diagram. The work is based on the Infrared Flux Method (Blackwell et al. 1990), which has proven useful for deriving temperatures of metal-poor giants of globular clusters (Arribas & Martínez-Roger 1987; Arribas et al. 1991), and has low dependence on models for these types of stars. The temperatures obtained are scaled to direct $T_{\rm eff}$ (Alonso et al. 1994a; Paper II). A thorough account of the procedure followed for the application of the method can be found in (Alonso et al. 1996a; Paper I) where we described a similar programme devoted to main sequence stars.

As an initial step, we selected a sample of stars ($\sim$ 500) covering a wide range in metal content (+0.5 > [Fe/H] > -3.0), and measured the infrared photometry JHK(L') required for the application of the IRFM (Alonso et al. 1998; Paper IV). The number of stars and their distribution in the parameters space is adequate for establishing reliable relations $T_{\rm eff}$-colour-[Fe/H] for giant stars. In this paper, we present the temperatures obtained. In a forthcoming paper, we will provide and discuss the calibrations $T_{\rm eff}$-colour-[Fe/H], as well as the mean intrinsic colours for giant stars.

The present paper is laid out as follows. In Sects. 2, 3 and 4, we outline the practical implementation of the IRFM: i.e. the calibration of $q \times R$-factors by using the grid of atmosphere models computed by Kurucz (1991, 1993); The determination and calibration of bolometric fluxes of giant stars by applying a method previously devised to obtain and calibrate bolometric fluxes of main sequence stars (Alonso et al. 1995; Paper III) and the description of the assignment of secondary atmospheric parameters to the stars of the sample. The effective temperatures are derived in Sect. 5, where we provide an analysis of the the internal consistency of the method and the uncertainties affecting the derived efective temperatures. In Sect. 6, temperatures derived in the present work are compared with those derived in previous works. In Sect. 7, results are summarized.