  Density-functional tight-binding and classical molecular dynamics simulations
are used to investigate the structural deformations and melting of planar
carbon nano-clusters $C_{N}$ with N=2-55. The minimum energy configurations for
different clusters are used as starting configuration for the study of the
temperature effects on the bond breaking/rotation in carbon lines (N$<$6),
carbon rings (5$<$N$<$19) and graphene nano-flakes. The larger the rings
(graphene nano-flake) the higher the transition temperature (melting point)
with ring-to-line (perfect-to-defective) transition structures. The melting
point was obtained by using the bond energy, the Lindemann criteria, and the
specific heat. We found that hydrogen-passivated graphene nano-flakes
(C$_{N}$H$_M$) have a larger melting temperature with a much smaller dependence
on its size. The edges in the graphene nano-flakes exhibit several different
meta-stable configurations (isomers) during heating before melting occurs.
