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We conjecture that the extra dimensions are physical non-compact at highenergy scale or high temperature; after the symmetry breaking or cosmologicalphase transition, the bulk cosmological constant may become negative, and then,the extra dimensions may become physical compact at low energy scale. We showthis in a five-dimensional toy brane model with three parallel 3-branes and areal bulk scalar whose potential is temperature dependent. We also point outthat after the global or gauge symmetry breaking, or the supersymmetry breakingin supergravity theory, the spontaneous physical compactification of the extradimensions might be realized.Comment: Latex, 7 pages, corrected typo in the footnot

SPONTANEOUS PHYSICAL COMPACTIFICATION OF THE EXTRA DIMENSIONS