  We study the thermodynamics of a quantum system interacting with different
baths in the repeated interaction framework. In an appropriate limit, the
evolution takes the Lindblad form and the corresponding thermodynamic
quantities are determined by the state of the full system plus baths. We
identify conditions under which the thermodynamics of the open system can be
described only by system properties and find a quantum local detailed balance
condition with respect to an equilibrium state that may not be a Gibbs state.
The three-qubit refrigerator introduced in [N. Linden, S. Popescu and P.
Skrzypczyk, Phys. Rev. Lett.$ {\bf 105}$, 130401 (2010)] is an example of such
a system. From a repeated interaction microscopic model we derive the Lindblad
equation that describes its dynamics and discuss its thermodynamic properties
for arbitrary values of the internal coupling between the qubits. We find that
external power (proportional to the internal coupling strength) is required to
bring the system to its steady state, but once there, it works autonomously as
discussed in [N. Linden, S. Popescu and P. Skrzypczyk, Phys. Rev. Lett. ${\bf
105}$, 130401 (2010)].
