Even tin isotopes of mass number A = 108-124 are calculated with realistic interactions in the generalized-seniority approximation of the nuclear shell model. For each nucleus, we compute the lowest 10 000 states (5000 of each parity) up to around 8 MeV in excitation energy, by allowing as many as four broken pairs. The lowest 50 eigen energies of each parity are compared with the exact results of the large-scale shell-model calculation. The wave functions of the midshell nuclei show a clear pattern of the stepwise breakup of condensed coherent pairs with increasing excitation energy. We also compute in the canonical ensemble the thermal properties-level density, entropy, and specific heat-in relation to the thermal pairing phase transition.