Wave Function Renormalization at Finite Temperature

We present a derivation of the medium dependent wave function renormalization for a spinor field in presence of a thermal bath. We show that, as already pointed out in literature, projector operators are not multiplicatively renormalized and the effect involves a non trivial spinor dependence, which disappears in the zero temperature covariant limit. The results, which differ from what already found in literature, are then applied to the decay of a massive scalar boson into two fermions and to the $\beta$--decay and crossed related processes relevant for primordial nucleosynthesis.