Molecular dynamics simulation with a Nose-Hoover thermostat was used to study melting and evaporation of free icosahedral argon clusters containing 13 to 1415 atoms. Clusters of 147 atoms or less were found to melt at temperatures clearly below the bulk melting temperature in agreement with previous results. Clusters containing 309 atoms or more were observed to desorb atoms at temperatures where the core of the cluster is solid. As a consequence of this a reliable determination of their melting temperatures using molecular dynamics was found to be complicated.