  We study internal work optimization over the energy levels of a generic hot
quantum Otto engine. We find universal features in the efficiency that
resembles the classical external power optimization over the coupling times to
the thermal baths. It is shown that in the ultra hot regime the efficiency is
determined solely by the optimization constraint, and independent of the engine
details. We show that for some constraints the radius of convergence of the
perturbative approach used in the classical analysis is zero even for very
arbitrarily low efficiencies at small temperature difference.
