  We investigate the coupling of an ensemble of phosphorus donors in an
isotopically purified $^{28}$Si host lattice interacting with a superconducting
coplanar waveguide resonator. The microwave transmission spectrum of the
resonator shows a normal mode splitting characteristic for high cooperativity.
The evaluated collective coupling strength $g_{\mathrm{eff}}$ is of the same
order as the loss rate of the spin system $\gamma$, indicating the onset of
strong coupling. We develop a statistical model to describe the influence of
temperature on the coupling strength from $50\,\mathrm{mK}$ to
$3.5\,\mathrm{K}$ and find a scaling of the coupling strength with the square
root of the number of thermally polarized spins.
