  In this paper we analyse the effect produced by the temperature in the vacuum
polarization associated with charged massless scalar field in the presence of
magnetic flux tube in the cosmic string spacetime. Three different
configurations of magnetic fields are taken into account: $(i)$ a homogeneous
field inside the tube, $(ii)$ a field proportional to $1/r$ and $(iii)$ a
cylindrical shell with $\delta$-function. In these three cases, the axis of the
infinitely long tube of radius $R$ coincides with the cosmic string. Because
the complexity of this analysis in the region inside the tube, we consider the
thermal effect in the region outside. In order to develop this analysis, we
construct the thermal Green function associated with this system for the three
above mentioned situations considering points in the region outside the tube.
We explicitly calculate in the high-temperature limit, the thermal average of
the field square and the energy-momentum tensor.
