Vacuum Polarization at Finite Temperature around a Magnetic Flux Cosmic String

We consider a general situation where a charged massive scalar field $\phi(x)$ at finite temperature interacts with a magnetic flux cosmic string. We determine a general expression for the Euclidean thermal Green's function of the massive scalar field and a handy expression for a massless scalar field. With this result, we evaluate the thermal average $<\phi^{2}(x)>$ and the thermal average of the energy-momentum tensor of a nonconformal massless scalar field.