  Context: A large number of the small and the short-lived EUV brightenings
have been detected in the quiet Sun (QS) over the past three years, by the High
Resolution Imager of the Extreme Ultraviolet Imager (HRIEUV) on board Solar
Orbiter. It is still uncertain whether these events reach coronal temperatures,
and thus if they directly participate to coronal heating.
  Aims: In this work, we evaluate the maximum temperature of 11 EUV
brightenings in the QS, through plasma diagnostics involving UV/EUV
spectroscopy and imaging.
  Methods: We use three QS observations coordinated between HRIEUV, the
Spectral Imaging of the Coronal Environment (SPICE/Solar Orbiter), the EUV
Imaging Spectrometer (EIS/Hinode), and the Atmospheric Imaging Assembly
(AIA/SDO). We detected events in HRIEUV, ranging from 0.8 to 6.2 Mm in length.
We then identified nine of them in SPICE and AIA, as well as three in EIS. We
investigated their temporal evolution using their light curves, and applied
temperature diagnostics, such as the LOCI Emission Measure (EM) and the
differential EM (DEM). We also estimated the electron density of one event
identified in EIS.
  Results: These events are dominated by emission of plasma at chromospheric
and TR temperatures, and they barely reach temperatures above 1 MK. As such, we
concluded that their contribution to coronal heating is not dominant. The
estimated density of one of the event is n$_e$ = (1.8 $\pm$ 1.3) $\times$
$10^{10}$ cm$^{-3}$.
