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We obtain three results: 1) Every compact simplex bundle with exactly onepoint in the fiber over 0 is the KMS bundle of a periodic flow on the Jiang-Sualgebra.  2) Let A be a separable unital C*-algebra with a unique trace state. Supposethat A tensorially absorbs the Jiang-Su algebra. The (weak) cocycle-conjugacyclasses of flows that are not approximately inner are uncountable.  3) Let B be a separable, simple, unital, purely infinite and nuclearC*-algebra in the UCT class. Assume that the K1 group of B is torsion free.Every proper simplex bundle with empty fiber over 0 is the KMS bundle of aperiodic flow on B.

On the bundle of KMS state spaces for flows on a Z-absorbing C*-algebra