  We have investigated the thorium (Th) abundance in a sample of 53 thin disc
solar twins covering a wide range of ages. These data provide constrains on the
mantle energy budget of terrestrial planets that can be formed over the
evolution of the Galaxy's thin disc. We have estimated Th abundances with an
average precision of 0.025\,dex (in both [Th/H] and [Th/Fe]) through
comprehensive spectral synthesis of a Th\,II line present at 4019.1290\,{\AA},
using very high resolution (R\,=\,115,000) high quality HARPS spectra obtained
at the ESO La Silla Observatory. We have confirmed that there is a large energy
budget from Th decay for maintaining mantle convection inside potential rocky
planets around solar twins, from the Galactic thin disc formation until now,
because the pristine [Th/H]$_{\rm ZAMS}$ is super-solar on average under a
uniform dispersion of 0.056\,dex (varying from +0.037 up to +0.138\,dex based
on linear fits against isochrone stellar age). Comparing to neodymium (Nd) and
europium (Eu), two others neutron-capture elements, the stellar pristine
abundance of Th follows Eu along the Galactic thin disc evolution, but it does
not follow Nd, probably because neodymium has a significant contribution from
the $s$-process (about 60\,per\,cent).
