  The celebrated exchange fluctuation theorem -- proposed by Jarzynski and
W\'ozcik, (Phys Rev. Lett. 92, 230602 (2004)) for heat exchange between two
systems in thermal equilibrium at different temperatures -- is explored here
for quantum Gaussian states in thermal equilibrium. We employ Wigner
distribution function formalism for quantum states, which exhibits close
resemblance with the classcial phase-space trajectory description, to arrive at
this theorem. For two Gaussian states in thermal equilibrium at two different
temperatures kept in contact with each other for a fixed duration of time we
show that the quantum Jarzyinski-W\'ozcik theorem agrees with the corresponding
classical result in the limit \hbar->0.
