  We study the classical and quantum KMS conditions within the context of spin
lattice systems. Specifically, we define a strict deformation quantization
(SDQ) for a $\mathbb{S}^2$-valued spin lattice system over $\mathbb{Z}^d$
generalizing the renown Berezin SDQ for a single sphere. This allows to promote
a classical dynamics on the algebra of classical observables to a quantum
dynamics on the algebra of quantum observables. We then compare the notion of
classical and quantum thermal equilibrium by showing that any weak*-limit point
of a sequence of quantum KMS states fulfils the classical KMS condition. In
short, this proves that the semiclassical limit of quantum thermal states
describes classical thermal equilibrium, strenghtening the physical
interpretation of the classical KMS condition. Finally we provide two
sufficient conditions ensuring uniqueness of classical and quantum KMS states:
The latter are based on an version of the Kirkwood-Salzburg equations adapted
to the system of interest. As a consequence we identify a mild condition which
ensures uniqueness of classical KMS states and of quantum KMS states for the
quantized dynamics for a common sufficiently high temperature.
