  We reconsider the composite string model introduced {30 years ago} to study
the vacuum energy. The model consists of a scalar field, describing the
transversal vibrations of a string consisting of piecewise constant sections
with different tensions and mass densities, keeping the speed of light constant
across the junctions. We consider the spectrum using transfer matrices and
Chebyshev polynomials to get a closed formula for the eigenfrequencies. We
calculate vacuum and free energy as well as the entropy of this system in two
approaches, one using contour integration and another one using a Hurwitz zeta
function. The latter results in a representation in terms of finite sums over
polynomials. Several limiting cases are considered as well, for instance, the
high-temperature expansion, which is expressed in terms of the heat kernel
coefficients. The vacuum energy has no ultraviolet divergences, and the
corresponding heat kernel coefficient $a_1$ is zero due to the constancy of the
speed of light. This is in parallel to a similar situation in macroscopic
electrodynamics with isorefractive boundary conditions.
