  Thermal conductivity ($\kappa$) of mantle minerals is a fundamental property
in geodynamic modeling. It controls the style of mantle convection and the time
scale of the mantle and core cooling. Cubic CaSiO$_3$ perovskite (CaPv) is the
third most abundant mineral in the lower mantle (LM) (7 vol%). However, despite
its importance, no theoretical or experimental estimate of CaPv's $\kappa$
exists. Theoretical investigations of its properties are challenging because of
its strong anharmonicity. Experimental measurements at relevant high pressures
and temperatures are equally challenging. Here we present $ab$ $initio$ results
for CaPv's $\kappa$ obtained using an established phonon quasiparticle approach
that can address its strong anharmonicity. We also offer experimental
measurements of $\kappa$. Predictions and measurements are in good agreement
and reveal a surprisingly large $\kappa$ for cubic CaPv. Despite its relatively
low abundance, CaPv's $\kappa$ might increase the lower mantle $\kappa$ by
approximately 10%, if accounted for. $\kappa$ of mantle regions enriched in
crust material will be more strongly impacted.
