  Measuring thermodynamic quantities can be easy or not, depending on the
system that is being studied. For a macroscopic object, measuring temperatures
can be as simple as measuring how much a column of mercury rises when in
contact with the object. At the small scale of quantum electromechanical
systems, such simple methods are not available and invariably detection
processes disturb the system state. Here we propose a method for measuring the
temperature on a suspended semiconductor membrane clamped at both ends. In this
method, the membrane is mediating a capacitive coupling between two
transmission line resonators (TLR). The first TLR has a strong dispersion, that
is, its decaying rate is larger than its drive, and its role is to pump in a
pulsed way the interaction between the membrane and the second TLR. By
averaging the pulsed measurements of the quadrature of the second TLR we show
how the temperature of the membrane can be determined. Moreover the statistical
description of the state of the membrane, which is directly accessed in this
approach is significantly improved by the addition of a Josephson Junction
coupled to the second TLR.
