  An explicit expression for the temperature of an open two-level quantum
system is obtained as a function of local properties, under the hypothesis of
weak interaction with the environment. This temperature is defined for both
equilibrium and out-of-equilibrium states, and coincides with the environment
temperature if the system reaches thermal equilibrium with a heat reservoir.
Additionally, we show that within this theoretical framework the total entropy
production can be partitioned into two contributions: one due to heat transfer,
and another, associated to internal irreversibilities, related to the loss of
internal coherence by the qubit. The positiveness of the heat capacity is
established, as well as its consistency with the well known results at thermal
equilibrium. We apply these concepts to two different systems, and show that
they behave in analogous ways as their classical counterparts.
