  The statistics of the heat exchanged between two quantum XX spin chains
prepared at different temperatures is studied within the assumption of weak
coupling. This provides simple formulas for the average heat and its
corresponding characteristic function, from which the probability distribu-
tion may be computed numerically. These formulas are valid for arbitrary sizes
and therefore allow us to analyze the role of the thermodynamic limit in this
non-equilibrium setting. It is found that all thermodynamic quantities are
extremely sensitive to the quantum phase transition of the XX chain.
