  We address the question of verifying the quantumness of thermal machines. A
Szil\'ard engine is truly quantum if its work output cannot be described by a
local hidden state (LHS) model, i. e. an objective local statistical ensemble.
Quantumness in this scenario is revealed by a steering-type inequality which
bounds the classically extractable work. A quantum Maxwell demon can violate
that inequality by exploiting quantum correlations between the work medium and
the thermal environment. While for a classical Szil\'ard engine an objective
description of the medium always exists, any such description can be ruled out
by a steering task in a truly quantum case.
