  We present a detailed study of the finite temperature dynamical properties of
the quantum Potts model in one dimension.Quasiparticle excitations in this
model have internal quantum numbers, and their scattering matrix {\gf deep} in
the gapped phases is shown to take a simple {\gf exchange} form in the
perturbative regimes. The finite temperature correlation functions in the
quantum critical regime are determined using conformal invariance, while {\gf
far from the quantum critical point} we compute the decay functions
analytically within a semiclassical approach of Sachdev and Damle [K. Damle and
S. Sachdev, Phys. Rev. B \textbf{57}, 8307 (1998)]. As a consequence, decay
functions exhibit a {\em diffusive character}. {\gf We also provide robust
arguments that our semiclassical analysis carries over to very low temperatures
even in the vicinity of the quantum phase transition.} Our results are also
relevant for quantum rotor models, antiferromagnetic chains, and some spin
ladder systems.
