We study the generation of lepton asymmetry in the superweak $U(1)_z$ extension of the standard model of particle interactions.
Special emphasis is put on the computation of the CP asymmetry factor
at finite temperature. We include contributions usually neglected in
the literature and evaluate their impact on leptogenesis. We find that
thermal effects are essential for the asymmetry factor, while
additional vertex cuts have negligible numerical impact on the lepton
asymmetry according to this model.

