= Solution
In an ordinary three-dimensional crystalline <electrical insulator>, heat is carried mainly by <phonons>. <Kinetic theory> gives the estimate
$$
\kappa\simeq\frac13 c_Vv_s\ell,
$$
where $c_V$ is <heat capacity> per unit <volume>, $v_s$ is a typical <sound speed>, and $\ell$ is the <phonon mean free path>. The <thermal conductivity> $\kappa$ has units $\mathrm{W\,m^{-1}\,K^{-1}}$.
At low <temperature>, $T\ll\Theta_D$, the <Debye model> gives $c_V\propto T^3$. With phonon-phonon collisions frozen out, diffuse scattering at the sample boundaries makes $\ell$ approximately constant, and $v_s$ is nearly constant. Hence
$$
\boxed{\kappa\propto T^3\quad\text{at low }T\text{ with boundary-limited scattering}.}
$$
At high <temperature>, of order or above the <Debye temperature>, the <Dulong-Petit law> makes $c_V$ approximately constant. Anharmonic <phonon scattering>, especially resistive <Umklapp scattering>, has a collision rate approximately proportional to $T$. Thus $\ell\propto T^{-1}$ and
$$
\boxed{\kappa\propto T^{-1}\quad\text{at high }T\text{ with Umklapp-limited scattering}.}
$$
These two regimes usually give an intermediate maximum of <thermal conductivity>. The assumptions matter: glassy materials, strong defects or specular boundary reflection can change the low-<temperature> law; these are not universal laws for every <electrical insulator>.
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