  We construct KMS-states from $\mathrm{Li}_1$-summable semifinite spectral
triples and show that in several important examples the construction coincides
with well-known direct constructions of KMS-states for naturally defined flows.
Under further summability assumptions the constructed KMS-state can be computed
in terms of Dixmier traces. For closed manifolds, we recover the ordinary
Lebesgue integral. For Cuntz-Pimsner algebras with their gauge flow, the
construction produces KMS-states from traces on the coefficient algebra and
recovers the Laca-Neshveyev correspondence. For a discrete group acting on its
Stone-\v{C}ech boundary, we recover the Patterson-Sullivan measures on the
Stone-\v{C}ech boundary for a flow defined from the Radon-Nikodym cocycle.
