We carry out a systematic investigation of the melting properties of Ar-12-HF (with HF in the ground vibrational state) using a classical Monte Carlo simulation enhanced by the j-walking algorithm. We discover two distinct features in the heat capacity of the system. The first feature around 11 K corresponds to the exchange of HF with one of the 12 surface atoms of the cluster. The second feature around 30 K corresponds to the melting of the argon frame. We investigate the spectrum of the cluster as a function of temperature using MC-MD methods and we find two distinct phenomena taking place gradually, each identifiable with a phase transition of the cluster. Optimization results reveal that the anisotropic Ar-HF interaction has large effects in the liquidlike structure of the cluster.