  The high temperature asymptotics of the Helmholtz free energy of
electromagnetic field subjected to boundary conditions with spherical and
cylindrical symmetries are constructed by making use of a general expansion in
terms of heat kernel coefficients and the related determinant. For this, some
new heat kernel coefficients and determinants had to be calculated for the
boundary conditions under consideration. The obtained results reproduce all the
asymptotics derived by other methods in the problems at hand and involve a few
new terms in the high temperature expansions. An obvious merit of this approach
is its universality and applicability to any boundary value problem correctly
formulated.
