  We study the performance of a quantum Otto cycle using a harmonic work medium
and undergoing collisional dynamics with finite-size reservoirs. We span the
dynamical regimes of the work strokes from strongly non-adiabatic to
quasi-static conditions, and address the effects that non-Markovianity of the
open-system dynamics of the work medium can have on the efficiency of the
thermal machine. While such efficiency never surpasses the classical upper
bound valid for finite-time stochastic engines, the behaviour of the engine
shows clear-cut effects induced by both the finiteness of the evolution time,
and the memory-bearing character of the system-environment evolution.
