Answer
The thermal conductivity of the material does not determine whether or not an electron is ejected.
Work Step by Step
We can state the photoelectric equation:
$hf = K_{max}+ \Phi$
$\Phi$ is the work function and it is a property of the target material. If energy is transferred from a photon to an electron such that $hf \gt \Phi$, then the electron can escape from the material.
The frequency of an individual photon determines whether or not an electron is ejected, but the thermal conductivity of the material does not.
