  We consider a semi-classical heat engine with a $q$-deformed quantum
oscillator working substance and classical thermal baths. We investigate the
influence of the quantum statistical deformation parameter $q$ on the work and
efficiency of the engine. In usual heat engines, a Hamiltonian parameter is
varied during the work injection and extraction stages while the quantum
statistical character of the working substance remains fixed. We point out that
even if the Hamiltonian parameters are not changing, work can be harvested by
quantum statistical changes of the working substance. Work extraction from
thermal resources using quantum statistical mutations of the working substance
makes a semi-classical engine cycle without any classical analog. As a concrete
example of such a semi-classical heat engine with a profound quantum character,
we consider the Otto cycle and use the deformation parameter to define the
isentropic steps while keeping the Hamiltonian parameters constant. We verify
that our conclusion applies to both bosonic and fermionic oscillator
deformations.
