  We consider a thermal quantum harmonic oscillator weakly coupled to a heat
bath at a different temperature. We analytically study the quantum heat
exchange statistics between the two systems using the quantum-optical master
equation. We exactly compute the characteristic function of the heat
distribution and show that it verifies the Jarzynski-W\'ojcik fluctuation
theorem. We further evaluate the heat probability density in the limit of long
thermalization times, both in the low and high temperature regimes, and
investigate its time evolution by calculating its first two cumulants.
