  We investigate the emergence of temperature $T$ in the system-plus-reservoir
paradigm starting from the fundamental microcanonical scenario at total fixed
energy $E$ where, contrary to the canonical approach, $T=T(E)$ is not a control
parameter but a derived auxiliary concept. As shown by Schwinger for the regime
of weak coupling $\gamma$ between subsystems, $T(E)$ emerges from the
saddle-point analysis leading to the ensemble equivalence up to corrections
${\cal O}(1/\sqrt{N})$ in the number of particles $N$ that defines the
thermodynamic limit. By extending these ideas for finite $\gamma$, while
keeping $N\to \infty$, we provide a consistent generalization of temperature
$T(E,\gamma)$ in strongly coupled systems and we illustrate its main features
for the specific model of Quantum Brownian Motion where it leads to consistent
microcanonical thermodynamics. Interestingly, while this $T(E,\gamma)$ is a
monotonically increasing function of the total energy $E$, its dependence with
$\gamma$ is a purely quantum effect notably visible near the ground state
energy, and for large energies differs for Markovian and non-Markovian regimes.
