  Starting from the Oliva--Tempo--Troncoso black hole, a solution of the
Bergshoeff--Hohm--Townsend massive gravity, a class of the Vaidya-like exact
vacuum solutions with torsion is constructed in the three-dimensional
Poincar\'e gauge theory. A particular subclass of these solutions is shown to
possess the asymptotic conformal symmetry. The related canonical energy
contains a contribution stemming from torsion.
