  A study of properties of the symmetry energy of nuclei is presented based on
density functional theory. Calculations for finite nuclei are given so that the
study includes isospin dependent surface symmetry considerations as well as
isospin independent surface effects. Calculations are done at both zero and
non-zero temperature. It is shown that the surface symmetry energy term is the
most sensitive to the temperature while the bulk energy term is the least
sensitive. It is also shown that the temperature dependence terms are
insensitive to the force used and even more insensitive to the existence of
neutron skin. Results for a symmetry energy with both volume and surface terms
are compared with a symmetry energy with only volume terms along the line of
$\beta$ stability. Differences of several MeV are shown over a good fraction of
the total mass range in $A$. Also given are calculations for the bulk, surface
and Coulomb terms.
