  We consider a chiral one-loop hedgehog soliton of the bosonized SU(2)$_f$
Nambu & Jona-Lasinio model which is embedded in a hot medium of constituent
quarks. Energy and radius of the soliton are determined in self-consistent
mean-field approximation. Quasi-classical corrections to the soliton energy are
derived by means of the pushing and cranking approaches. The corresponding
inertial parameters are evaluated. It is shown that the inertial mass is
equivalent to the total internal energy of the soliton. Corrected nucleon and
$\Delta$ isobar masses are calculated in dependence on temperature and density
of the medium. As a result of the self-consistently determined internal
structure of the soliton the scaling between constituent quark mass, soliton
mass and radius is noticeably disturbed.
