  Total vacuum energy of some quantized fields in conical space with additional
boundary conditions is calculated. These conditions are imposed on a
cylindrical surface which is coaxial with the symmetry axis of conical space.
The explicit form of the matching conditions depends on the field under
consideration. In the case of electromagnetic field, the perfectly conducting
boundary conditions or isorefractive matching conditions are imposed on the
cylindrical surface. For a massless scalar field, the semi-transparent
conditions ($\delta$-potential) on the cylindrical shell are investigated. As a
result, the total Casimir energy of electromagnetic field and scalar field, per
a unit length along the symmetry axis, proves to be finite unlike the case of
an infinitely thin cosmic string. In these studies the spectral zeta functions
are widely used. It is shown briefly how to apply this technique for obtaining
the asymptotics of the relevant thermodynamical functions in the high
temperature limit.
