  We report the measurements of the thermal conductivity ($\kappa$) of iron
(Fe) and nickel (Ni) at high pressures and high temperatures. $\kappa$ values
are estimated from the temperature measurements across the sample surface in a
laser heated diamond anvil cell (LHDAC) and using the COMSOL software.
Near-isothermal $\kappa$'s are observed to increase with pressure in both the
metals due to the increase of density of the pressed metals. In both metals
$\kappa$'s are observed to follow a sharp fall during melting at different
pressure points and are consistence with the other multi-anvil measurements.
Constant values of $\kappa$ in these metals during melting at different
pressures reveal the loss of long range order, which creates independent
movement of atomic metals. The melting temperature measured in these metals
from the sudden drop of $\kappa$-values are in a good agreement with the other
melting measurements in LHDAC. The results obtained in this study is expected
to provide an insight to the studies on the planets Mercury and Mars and their
interior.
