  The finite temperature behavior of small Silicon (Si$_{10}$, Si$_{15}$, and
Si$_{20}$) and Tin (Sn$_{10}$ and Sn$_{20}$) clusters is studied using
isokinetic Born-Oppenheimer molecular dynamics. The lowest equilibrium
structures of all the clusters are built upon a highly stable tricapped
trigonal prism unit which is seen to play a crucial role in the finite
temperature behavior of these clusters. Thermodynamics of small tin clusters
(Sn$_{10}$ and Sn$_{20}$) is revisited in light of the recent experiments on
tin clusters of sizes 18-21 [G. A. Breaux et. al. Phys. Rev. B {\bf 71} 073410
(2005)]. We have calculated heat capacities using multiple histogram technique
for Si$_{10}$, Sn$_{10}$ and Si$_{15}$ clusters. Our calculated specific heat
curves have a main peak around 2300 K and 2200 K for Si$_{10}$ and Sn$_{10}$
clusters respectively. However, various other melting indicators such as root
mean square bond length fluctuations, mean square displacements show that
diffusive motion of atoms within the cluster begins around 650 K. The finite
temperature behavior of Si$_{10}$ and Sn$_{10}$ is dominated by isomerization
and it is rather difficult to discern the temperature range for transition
region. On the other hand, Si$_{15}$ does show a liquid like behavior over a
short temperature range followed by the fragmentation observed around 1800 K.
Finite temperature behavior of Si$_{20}$ and Sn$_{20}$ show that these clusters
do not melt but fragment around 1200 K and 650 K respectively.
