  We present an analysis of the temperature dependence of the optical response
of small sodium clusters in a temperature range bracketing the melting phase
transition. When the temperature increases, the mean excitation energy
undergoes a red shift and the plasmon is significantly broadened, in agreement
with recent experimental data. We show that the single--particle levels acquire
a prominent width and the HOMO--LUMO gap as well as the width of the occupied
band are reduced due to large thermal cluster size and shape fluctuations. This
results in a sharp increase of the static polarizability with temperature.
