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We deduce the relation between the critical temperature associated to thesymmetry breaking of scalar fields with one--loop correction potential immersedin a thermal bath and the condensation temperature of the aforementionedsystem, assuming a harmonic oscillator type potential. We show that these twotemperatures are related through the \emph{scale} associated to the system. Inthis aim, we infer the order of magnitude for the \emph{scale} as a function ofthe corresponding healing length, in order to give a criterium to compare bothtemperatures. Additionally, we prove that the condensation temperature isindependent of the thermal bath within the semiclassical approximation, for apositive coupling constant, assuming that the thermal bath contribution is thelowest energy associated to the system.

Critical Temperature Associated to Symmetry Breaking of Klein--Gordon  fields versus Condensation Temperature in a Weakly interacting Bose--Einstein  Gas