  {Chromospheric evaporation is a key process in solar flares that has
extensively been investigated using the spectroscopic observations. However,
direct soft X-ray (SXR) imaging of the process is rare, especially in remote
brightenings associated with the primary flares that have recently attracted
dramatic attention.} {We intend to find the evidence for chromospheric
evaporation and figure out the cause of the process in sympathetic coronal
bright points (CBPs), i.e., remote brightenings induced by the primary CBP.}
{We utilise the high-cadence and high-resolution SXR observations of CBPs from
the X-ray Telescope (XRT) aboard the Hinode spacecraft on 2009 August 23.} {We
discover thermal conduction front propagating from the primary CBP, i.e., BP1,
to one of the sympathetic CBPs, i.e., BP2 that is 60$\arcsec$ away from BP1.
The apparent velocity of the thermal conduction is $\sim$138 km s$^{-1}$.
Afterwards, hot plasma flowed upwards into the loop connecting BP1 and BP2 at a
speed of $\sim$76 km s$^{-1}$, a clear signature of chromospheric evaporation.
Similar upflow was also observed in the loop connecting BP1 and the other
sympathetic CBP, i.e., BP3 that is 80$\arcsec$ away from BP1, though less
significant than BP2. The apparent velocity of the upflow is $\sim$47 km
s$^{-1}$. The thermal conduction front propagating from BP1 to BP3 was not well
identified except for the jet-like motion also originating from BP1.} {We
propose that the gentle chromospheric evaporation in the sympathetic CBPs were
caused by thermal conduction originating from the primary CBP.}
