  Ongoing experimental activity aims at calorimetric measurements of
thermodynamic indicators of quantum integrated systems. We study a model of a
driven qubit in contact with a finite-size thermal electron reservoir. The
temperature of the reservoir changes due to energy exchanges with the qubit and
an infinite-size phonon bath. Under the assumption of weak coupling and weak
driving, we model the evolution of the qubit-electron-temperature as a hybrid
master equation for the density matrix of the qubit at different temperatures
of the calorimeter. We compare the temperature evolution with an earlier
treatment of the qubit-electron model, where the dynamics were modelled by a
Floquet master equation under the assumption of drive intensity much larger
than the qubit-electron coupling squared. We numerically and analytically
inquire the predictions of the two mathematical models of dynamics in the
weak-drive parametric region. We numerically determine the parametric regions
where the two models of dynamics give distinct temperature predictions and
those where their predictions match.
