  We report the thermodynamic properties of an ideal boson gas confined in an
infinite periodic array of channels modeled by two, mutually perpendicular,
Kronig-Penney delta-potentials. The particle's motion is hindered in the x-y
directions, allowing tunneling of particles through the walls, while no
confinement along the z direction is considered. It is shown that there exists
a finite Bose- Einstein condensation (BEC) critical temperature Tc that
decreases monotonically from the 3D ideal boson gas (IBG) value $T_{0}$ as the
strength of confinement $P_{0}$ is increased while keeping the channel's cross
section, $a_{x}a_{y}$ constant. In contrast, Tc is a non-monotonic function of
the cross-section area for fixed $P_{0}$. In addition to the BEC cusp, the
specific heat exhibits a set of maxima and minima. The minimum located at the
highest temperature is a clear signal of the confinement effect which occurs
when the boson wavelength is twice the cross-section side size. This
confinement is amplified when the wall strength is increased until a
dimensional crossover from 3D to 1D is produced. Some of these features in the
specific heat obtained from this simple model can be related, qualitatively, to
at least two different experimental situations: $^4$He adsorbed within the
interstitial channels of a bundle of carbon nanotubes and
superconductor-multistrand-wires Nb$_{3}$Sn.
