  A recent stacking analysis of Planck HFI data of galaxy clusters (Hurier
2016) allowed to derive the cluster temperatures by using the relativistic
corrections to the Sunyaev-Zel'dovich effect (SZE). However, the temperatures
of high-temperature clusters, as derived from this analysis, resulted to be
basically higher than the temperatures derived from X-ray measurements, at a
moderate statistical significance of $1.5\sigma$. This discrepancy has been
attributed by Hurier (2016) to calibration issues. In this paper we discuss an
alternative explanation for this discrepancy in terms of a non-thermal SZE
astrophysical component. We find that this explanation can work if non-thermal
electrons in galaxy clusters have a low value of their minimum momentum
($p_1\sim0.5-1$), and if their pressure is of the order of $20-30\%$ of the
thermal gas pressure. Both these conditions are hard to obtain if the
non-thermal electrons are mixed with the hot gas in the intra cluster medium,
but can be possibly obtained if the non-thermal electrons are mainly confined
in bubbles with high content of non-thermal plasma and low content of thermal
plasma, or in giant radio lobes/relics located in the outskirts of clusters. In
order to derive more precise results on the properties of non-thermal electrons
in clusters, and in view of more solid detections of a discrepancy between
X-rays and SZE derived clusters temperatures that cannot be explained in other
ways, it would be necessary to reproduce the full analysis done by Hurier
(2016) by adding systematically the non-thermal component of the SZE.
