The off-equilibrium probability distribution of the heat exchanged by a ferromagnet in a time interval after a quench below the critical point is calculated analytically in the large-N limit. Here N is the number of components of the vectorial order parameter. The distribution shows a singular behavior with a critical threshold below which a macroscopic fraction of heat is released by the k=0 Fourier mode of the order parameter. The mathematical structure producing this phenomenon is the same responsible of the order parameter condensation in the equilibrium low temperature phase. The heat exchanged by the individual Fourier modes follows a non trivial pattern, with the unstable modes at small wave vectors warming up the modes around a characteristic finite wave vector k_M. Two internal temperatures, associated to the k=0 and k=k_M modes, rule the heat currents through a fluctuation relation similar to the one for stationary systems in contact with two thermal reservoirs.
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