  We report the results of detailed thermodynamic investigations of the
Sn$_{20}$ cluster using density-functional molecular dynamics. These
simulations have been performed over a temperature range of 150 to 3000 K, with
a total simulation time of order 1 ns. The prolate ground state and low-lying
isomers consist of two tricapped trigonal prism (TTP) units stacked end to end.
The ionic specific heat, calculated via a multihistogram fit, shows a small
peak around 500 K and a shoulder around 850 K. The main peak occurs around 1200
K, about 700 K higher than the bulk melting temperature, but significantly
lower than that for Sn$_{10}$. The main peak is accompanied by a sharp change
in the prolate shape of the cluster due to the fusion of the two TTP units to
form a compact, near spherical structure with a diffusive liquidlike ionic
motion. The small peak at 500 K is associated with rearrangement processes
within the TTP units, while the shoulder at 850 K corresponds to distortion of
at least one TTP unit, preserving the overall prolate shape of the cluster. At
all temperatures observed, the bonding remains covalent.
