We investigate by means of a variational approach the effective potential of a 5D U(1) scalar model at finite temperature and compactified on S^1 and S^1/Z_2 as well as the corresponding 4D model obtained through a trivial dimensional reduction. We are particularly interested in the behaviour of the thermal masses of the scalar field with respect to the Wilson line phase and the results obtained are compared with those coming from a one-loop effective potential calculation. We also explore the nature of the phase transition.
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