  We aim to give a pedagogic presentation of the open system dynamics of a
periodically driven qubit in contact with a temperature bath. We are
specifically interested in the thermodynamics of the qubit. It is well known
that by combining the Markovian approximation with Floquet theory it is
possible to derive a stochastic Schr\"odinger equation in $\mathbb{C}^2$ for
the state of the qubit. We follow here a different approach. We use Floquet
theory to embed the time-non autonomous qubit dynamics into time-autonomous yet
infinite dimensional dynamics. We refer to the resulting infinite dimensional
system as the dressed-qubit. Using the Markovian approximation we derive the
stochastic Schr\"odinger equation for the dressed-qubit. The advantage of our
approach is that the jump operators are ladder operators of the Hamiltonian.
This simplifies the formulation of the thermodynamics. We use the
thermodynamics of the infinite dimensional system to recover the
thermodynamical description for the driven qubit. We compare our results with
the existing literature and recover the known results.
