  We present the general theory of a quantum heat machine based on an $N$-level
system (working medium) whose $N-1$ excited levels are degenerate, a
prerequisite for steady-state interlevel coherence. Our goal is to find out: To
what extent is coherence in the working medium an asset for heat machines? The
performance bounds of such a machine are common to (reciprocating) cycles that
consist of consecutive strokes and continuous cycles wherein the periodically
driven system is constantly coupled to cold and hot heat baths. Intriguingly,
we find that the machine's performance strongly depends on the relative
orientations of the transition-dipole vectors in the system. Perfectly aligned
(parallel) transition dipoles allow for steady-state coherence effects, but
also give rise to dark states, which hinder steady-state thermalization and
thus reduce the machine's performance. Similar thermodynamic properties hold
for $N$ two-level atoms conforming to the Dicke model. We conclude that level
degeneracy, but not necessarily coherence, is a thermodynamic resource, equally
enhancing the heat currents and the power output of the heat machine. By
contrast, the efficiency remains unaltered by this degeneracy and adheres to
the Carnot bound.
