  The determination of stellar effective temperature ($T_{\mathrm{eff}}$) in F,
G, and K stars using H$\alpha$ profile fitting is a quite remarkable and
powerful tool, because it practically does not depend on other atmospheric
parameters and reddening. Nevertheless, this technique is not frequently used
because of the complex procedure to recover the profile of broad lines in
echelle spectra. As a consequence, tests performed on different models have
sometimes provided ambiguous results. We have developed a normalization method
for recovering undistorted H$\alpha$ profiles and we have first applied it to
spectra acquired with the single order instrument at do Pico dos Dias
Observatory to avoid the problem of blaze correction. The continuum location is
optimized using an iterative procedure, where the identification of minute
telluric features is performed. A set of spectra was acquired with the MUSICOS
echelle spectrograph ($R = 40~000$) to independently validate the normalization
method. The accuracy of the method and of the 1D + LTE model is determined
using coud\'{e}/HARPS/MUSICOS spectra of the Sun and a sample of 10 Gaia
Benchmark Stars with effective temperature determined from interferometric
measurements. We find that the most used solar atlases cannot be used as
templates for H$\alpha$ temperature diagnostics without renormalization. The
comparison with the Sun shows that $T_{\mathrm{eff}}$ derived with H$\alpha$
profiles from 1D + LTE models underestimate the solar effective temperature by
28 K. Interferometry and Infrared Flux Method show a dependency on metallicity
according to the relation $T_{\mathrm{eff}} = T_{\mathrm{eff}}^{H\alpha}$
$-159$[Fe/H] + 28 K within the metallicity range $-0.7$ to $+0.45$ dex. We find
3D models largely improve the agreement with the interferometric and Infrared
Flux Method measurements.
