The determination of stellar effective temperature (T_eff_) in F, G, and K stars using Halpha profile fitting is a quite remarkable and powerful tool because it does not depend on reddening and is only slightly sensitive to other atmospheric parameters. Nevertheless, this technique is not frequently used because of the complex procedure needed to recover the profile of broad lines in echelle spectra. As a consequence, tests performed on different models have sometimes provided ambiguous results. The main aim of this work is to test the ability of the Halpha profile fitting technique to derive T_eff. We also aim to improve the applicability of this technique to echelle spectra and to test how well 1D+LTE models perform on a variety of F-K stars. We also apply the technique to HARPS spectra and test the reliability and the stability of the HARPS response over several years using the Sun. We have developed a normalization method for recovering undistorted Halpha profiles and we have first applied it to spectra acquired with the single-order coude instrument (resolution R=45000) at do Pico dos Dias Observatory to avoid the problem of blaze correction. The continuum location around Halpha is optimised using an iterative procedure, where the identification of minute telluric features is performed. A set of spectra was acquired with the MUSICOS echelle spectrograph (R=40000) to independently validate the normalization method. The accuracy of the method and of the 1D+LTE model is determined using coude/HARPS/MUSICOS spectra of the Sun and coude-only spectra of a sample of ten Gaia Benchmark Stars with T_eff_ determined from interferometric measurements. HARPS, coude, and MUSICOS spectra are used to determine T_eff_ of 43 sample stars. We find that a proper choice of spectral windows of fits plus the identification of telluric features allow for a very careful normalization of the spectra and produce reliable H{alpha} profiles. We also find that the most used solar atlases cannot be used as templates for Halpha temperature diagnostics without renormalization. The comparison with the Sun shows that H{alpha} profiles from 1D+LTE models underestimate the solar T_eff_ by 28K. We find the same agreement between Halpha and interferometry and between Halpha and Infrared Flux Method: a shallow dependency on metallicity according to the relation T_eff_=T_eff_^Halpha^-159[Fe/H]+28K within the metallicity range -0.70 to +0.40dex. The comparison with the Infrared Flux Method shows a scatter of 59K dominated by photometric errors (52K). In order to investigate the origin of this dependency, we analysed spectra from 3D models and found that they produce hotter temperatures, and that their use largely improves the agreement with the interferometric and Infrared Flux Method measurements. Finally, we find HARPS spectra to be fully suitable for Halpha profile temperature diagnostics; they are perfectly compatible with the coude spectra, and lead to the same T_eff_ for the Sun as that found when analysing HARPS spectra over a timespan of more than 7 years.

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