  Here we analyze the finite temperature expectation values of the charge and
current densities for a massive fermionic quantum field with nonzero chemical
potential, $\mu$, induced by a magnetic flux running along the axis of an
idealized cosmic string. These densities are decomposed into the vacuum
expectation values and contributions coming from the particles and
antiparticles. Specifically the charge density is an even periodic function of
the magnetic flux with the period equal to the quantum flux and an odd function
of the chemical potential. The only nonzero component of the current density
corresponds to the azimuthal current and it is an odd periodic function of the
magnetic flux and an even function of the chemical potential. Both analyzed are
developed for the cases where $|\mu |$ is smaller than the mass of the field
quanta, $m$.
