  We study collective excitations of a trapped Fermi gas at finite temperature
using the Bogoliubov-deGennes mean-field theory in conjunction with the
generalized random phase approximation. The collective excitations are analyzed
through the density response of a monopole excitation. We show the appearance
of several modes at the normal fluid - superfluid phase transition temperature:
Higgs mode-like pairing amplitude modulations, analogues of the second sound in
the trapped gas, and an edge mode that is also the strongest mode in the
response.
