  As optical clocks are improved to reach the frequency uncertainty below the
10$^{-17}$ level, the frequency shift due to the blackbody radiation (BBR) has
been one of the major systematic effects hindering further improvement. To
evaluate the BBR shift of an Yb optical lattice clock at KRISS, we installed an
in-vacuum BBR shield and made radiation thermometry using a black-coated-sphere
thermal probe. After we quantitatively measured the conduction loss of the
thermal probe and the effects of all the external radiation sources, we
determined the temperature at the atom trap site with an uncertainty of 13 mK,
which corresponds to an uncertainty of 0.22 mHz in the clock frequency (a
fractional frequency of $4.2\times10^{-19}$). The total uncertainty of the BBR
shift including the atomic response is $9.5\times10^{-19}$.
