We calculate the static dipole polarizability at finite temperature of sodi
um clusters of size 8, 20, 40, 55, 93, and 139 using an extended Thomas-Fer
mi description of the valence electrons. We find polarizabilities at 300 K
that are roughly 15% greater than at 0 K, consistent with discrepancies bet
ween theoretical polarizabilities at OK;ind measured polarizabilities. We p
redict that a sharp rise in the polarizability, of about 5%, occurs for siz
es of 55 and 139 when the cluster melts, offering the possibility of an alt
ernative method for measuring cluster melting points.