  The ro--vibrational spectra of molecules dissolved in liquid $^4$He
nanodroplets display rotational structure. Where resolved, this structure has
been used to determine a temperature that has been assumed to equal that of the
intrinsic excitations of the helium droplets containing the molecules.
Consideration of the density of states as a function of energy and total
angular momentum demonstrates that there is a small but significant bias of the
rotor populations that make the temperature extracted from a fit to its
rotational level populations slightly higher than the temperature of the
ripplons of the droplet. This bias grows with both the total angular momentum
of the droplet and with the moment of inertia of the solute molecule.
