RR Lyrae pulsational temperature scales: on the consistency between different empirical relations

In this paper, by assuming the equilibrium temperatures of RRab Lyrae variables defined by Carney, Storm & Jones as correct we show that temperatures derived from (B-V) colour (mean colour over the pulsational cycle calculated on the magnitude scale) transformations by Bessel, Castelli & Plez are consistent with the Carney et al. equilibrium temperatures within a probable error of δlogT_e=+/-0.003. As a consequence, it is shown that the pulsational temperature scale temperature-period-blue amplitude [T_eff=f(P,A_B)] relation provided by De Santis, who studied the (B-V) colour of about 70 stars of Lub's sample, is a suitable relation, being reddening- and metallicity-free, to calculate equilibrium temperatures for RRab variables. This relation is independent of variable mass and luminosity within a large range of period-shift from the mean period-amplitude relation valid for Lub's sample of variables. On the contrary, it is also shown that a temperature-amplitude-metallicity relation is strictly dependent on the period-amplitude relation of the sample used for calibrating it: we prove that this means it is dependent on both the mass and luminosity variations of variables.