  The isoscaling properties of isotopically resolved projectile residues from
peripheral collisions of 86Kr (25 MeV/nucleon), 64Ni (25 MeV/nucleon) and 136Xe
(20 MeV/nucleon) beams on various target pairs are employed to probe the
symmetry energy coefficient of the nuclear binding energy. The present study
focuses on heavy projectile fragments produced in peripheral and semiperipheral
collisions near the onset of multifragment emission E*/A = 2-3 MeV). For these
fragments, the measured average velocities are used to extract excitation
energies. The excitation energies, in turn, are used to estimate the
temperatures of the fragmenting quasiprojectiles in the framework the Fermi gas
model. The isoscaling analysis of the fragment yields provided the isoscaling
parameters "alpha" which, in combination with temperatures and isospin
asymmetries provided the symmetry energy coefficient of the nuclear binding
energy of the hot fragmenting quasiprojectiles. The extracted values of the
symmetry energy coefficient at this excitation energy range (2-3 MeV/nucleon)
are lower than the typical liquid-drop model value ~25 MeV corresponding to
ground-state nuclei and show a monotonic decrease with increasing excitation
energy. This result is of importance in the formation of hot nuclei in
heavy-ion reactions and in hot stellar environments such as supernova.
