  Precision measurements of quantum systems often seek to probe or must account
for the interaction with blackbody radiation. Over the past several decades,
much attention has been given to AC Stark shifts and stimulated state transfer.
For a blackbody in thermodynamic equilibrium, these two effects are determined
by the expectation value of photon number in each mode of the Planck spectrum.
Here, we explore how the photon number variance of an equilibrium blackbody
generally leads to a parametric broadening of the energy levels of quantum
systems that is inversely proportional to the square-root of the blackbody
volume. We consider the the effect in two cases which are potentially highly
sensitive to this broadening: Rydberg atoms and atomic clocks. We find that
even in blackbody volumes as small as 1\,cm$^3$, this effect is unlikely to
contribute meaningfully to transition linewidths.
