  The first order correction to the parton fragmentation functions in a thermal
medium is derived in the leading logarithmic approximation in the framework of
thermal field theory. The medium-modified evolution equations of the parton
fragmentation functions are also derived. It is shown that all infrared
divergences, both linear and logarithmic, in the real processes are canceled
among themselves and by corresponding virtual corrections. The evolution of the
quark number and the energy loss (or gain) induced by the thermal medium are
investigated.
