  The Gaia DR3 release includes heliocentric radial velocity measurements and
velocity variability indices for tens of millions of stars observed over 34
months.In this study, we utilise these indices to investigate the intrinsic
radial velocity variations of Hydrogen-deficient Carbon (HdC) stars and Extreme
Helium (EHe) stars across their large ranges of temperature and brightness.
Taking advantage of the newly defined HdC temperature classes, we examine the
evolution of the total velocity amplitude with effective temperature.
Additionally, we analyse the variation in the dust production rate of R Coronae
Borealis (RCB) stars with temperature using two different proxies for the
photometric state of RCB stars: one from Gaia and another from the 2MASS
survey. Our observations revealed a trend in the evolution of the maximum
radial velocity amplitude across each HdC temperature class. Similarly, we also
observed a correlation between stellar temperature and the dust production
rate. Interestingly, we possibly observed for the first time some variations of
the intrinsic radial velocity amplitude and the dust production rate with HdC
temperature class. If confirmed, these variations would indicate that the
helium shell-burning giant stage starts with strong atmospheric motions that
decrease in strength, up to $\sim$6000 K, before picking up again as the HdC
star atmosphere shrinks further in size and reaches warmer temperatures.
Moreover, the dust formation rate appears to be much higher in colder RCB stars
compared to warmer ones.
