  Here we analyze the expectation value of the fermionic condensate and the
energy-momentum tensor associated with a massive charged fermionic quantum
field with a nonzero chemical potential propagating in a magnetic-flux-carrying
cosmic string with compactified dimension in thermal equilibrium at finite
temperature $T$. We assume that, in addition to the magnetic field flux running
along the string's core, a magnetic flux enclosed by the compact dimension is
presented, and the field interacts with both. The expectation values of the
fermionic condensate and the energy-momentum tensor are expressed as the sum of
vacuum expectation values and the finite temperature contributions coming from
the particles and antiparticles excitation. As consequence of the
compactification, the thermal corrections of these observable are decomposed in
a part induced by pure cosmic string spacetime, plus a contribution induced by
the compactification. The thermal expectations values of the fermionic
condensate and the energy-momentum tensor are even periodic functions of the
magnetic flux with period being the quantum flux, and also even functions of
the chemical potential. Because the analyses of vacuum expectation of the
fermionic condensate and energy-momentum tensor have been developed in
literature, here we are mainly interested in the investigation of the thermal
corrections. In this way we explicitly study how these observable behaves in
the limits of low and high temperatures, and also for points near the string.
Besides the analytical discussions, we included some graphs that exhibit the
behavior of these observable for different values of the physical parameters of
the model.
