  In this paper we study the expectation values of the induced charge and
current densities for a massive bosonic field with nonzero chemical potential
in the geometry of a higher dimensional compactified cosmic string with
magnetic fluxes, along the string core and also enclosed by the compactified
direction, in thermal equilibrium at finite temperature $T$. These densities
are calculated by decomposing them into the vacuum expectation values and
finite temperature contributions coming from the particles and antiparticles.
The only nonzero components correspond to the charge, azimuthal and axial
current densities. By using the Abel-Plana formula, we decompose the components
of the densities into the part induced by the cosmic string and the one by the
compactification. The charge density is an odd function of the chemical
potential and even periodic function of the magnetic flux with a period equal
to the quantum flux. Moreover, the azimuthal (axial) current density is an even
function of the chemical potential and an odd (even) periodic function of the
magnetic flux with the same period. In this paper our main concern is the
thermal effect on the charge and current densities, including some limiting
cases, the low and high temperature approximations. We show that in all cases
the temperature enhances the induced densities.
