  A Bethe ansatz equation associated with the Lie superalgebra osp(1|2s) is
studied. A thermodynamic Bethe ansatz (TBA) equation is derived by the string
hypothesis. The high temperature limit of the entropy density is expressed in
terms of the solution of the osp(1|2s) version of the Q-system. In particular
for fundamental representation case, we also derive a TBA equation from the
osp(1|2s) version of the T-system and the quantum transfer matrix method. This
TBA equation is identical to the one from the string hypothesis. The central
charge is expressed by the Rogers dilogarithmic function, and identified to s.
