We have mapped from the quantum to the classical limit the spin excitation spectrum of the antiferromagnetic spin-1 Heisenberg chain system ${\mathrm{CsNiCl}}_3$ in its paramagnetic phase from $T=5\mathrm{}$ to $200\mathrm{K}.$ Neutron scattering shows that the excitations are resonant and dispersive up to at least $T=70\mathrm{}\mathrm{K}\simeq 2.7J,$ but broaden considerably with increasing temperature. The dispersion flattens out with increasing temperature as the resonance energy $\Delta$ at the antiferromagnetic wave vector increases and the maximum in the dispersion decreases. The correlation length $\xi$ between $T=12\mathrm{}$ and $50\mathrm{K}$ is in agreement with quantum Monte Carlo calculations for the spin-1 chain. $\xi$ is also consistent with the single mode approximation, suggesting that the excitations are short-lived single particle excitations. Below $T=12\mathrm{}\mathrm{K}$ where three-dimensional spin correlations are important, $\xi$ is shorter than predicted and the experiment is not consistent with the random phase approximation for coupled quantum chains. At $T=200\mathrm{}\mathrm{K},$ the structure factor and second energy moment of the excitation spectrum are in excellent agreement with the high-temperature series expansion.