The first order correction to the parton fragmentation functions in a thermal medium is derived in the leading logarithmic approximationin 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.