  By leveraging the Variational Quantum Eigensolver (VQE), the ``quantum
equation of motion" (qEOM) method established itself as a promising tool for
quantum chemistry on near term quantum computers, and has been used extensively
to estimate molecular excited states. Here, we explore a novel application of
this method, employing it to compute thermal averages of quantum systems,
specifically molecules like ethylene and butadiene. A drawback of qEOM is that
it requires measuring the expectation values of a large number of observables
on the ground state of the system, and the number of necessary measurements can
become a bottleneck of the method. In this work we focus on measurements
through informationally complete positive operator-valued measures (IC-POVMs)
to achieve a reduction in the measurements overheads. We show with numerical
simulations that the qEOM combined with IC-POVM measurements ensures a
satisfactory accuracy in the reconstruction of the thermal state with a
reasonable number of shots.
