The spin dynamics of the 1D antiferromagnetic Heisenberg system Y2BaNi1-xZnxO5 has been investigated by thermal (for x = 0) and cold (for x = 0.01 and 0.03) neutron scattering. The former set of measurements enables us to study the temperature dependence of the transitions from the ground state to states above the Haldane gap. The latter, low incident energy measurements, reveal a quasielastic component in the spectra which shows an activated temperature behaviour and a strong dependence on the chain length. We suggest a mechanism which could be the origin of the present observations.