  We investigate KMS states of Fowler's Nica-Toeplitz algebra $\mathcal{NT}(X)$
associated to a compactly aligned product system $X$ over a semigroup $P$ of
Hilbert bimodules. This analysis relies on restrictions of these states to the
core algebra which satisfy appropriate scaling conditions. The concept of
product system of finite type is introduced. If $(G, P)$ is a lattice ordered
group and $X$ is a product system of finite type over $P$ satisfying certain
coherence properties, we construct KMS$_\beta$ states of $\NT(X)$ associated to
a scalar dynamics from traces on the coefficient algebra of the product system.
Our results were motivated by, and generalize some of the results of Laca and
Raeburn obtained for the Toeplitz algebra of the affine semigroup over the
natural numbers.
