  REBCO coated conductors (CCs) have the potential to widen considerably the
application areas of superconductivity. Quench protection of REBCO-based
devices represents one of the major obstacles to this expansion. Thermal
conductivity data are mandatory ingredients for quench simulation studies. In
particular, the transverse thermal conductivity ($\kappa_T$) of the CC plays a
key role in case of quenches in superconducting magnets. In the present work,
we report $\kappa_T$ of thermally stabilized REBCO CCs produced by different
manufacturers. We have measured $\kappa_T$ on single CCs rather than on stacks
of soldered tapes, this excludes spurious contributions in the measurements. We
have found that the presence of the stabilizer at the tape edges in
Cu-electroplated CCs increases the overall $\kappa_T$. In the absence of this
effect, the overall thermal resistance is dominated by the substrate.
