By means of the optimized expansion technique, the D + 1-dimensional quantum sine-Gordon （sG） field theory is studied nonperturbatively for both zero and finite temperatures.In 1 + 1 and 2+ 1 dimensions, the theory is finite when momentum cutoff Λ tends to infinity.The temperature-dependent Coleman phase transition conditions we obtained reduce to theknown results gcr2 =8π for 1+ 1 dimensions and gcr2= 16π/mRO for 2+ 1 dimensions whenT→0. Especially, gcr tends to zero at T→∞ limit both for 1 + 1 and 2 + 1 dimensions. Thereis no critical temperature making the Φ= 0 vacuum unstable. In 3 + 1 dimensions, if g2 isfinite and Λ→∞, the theory is trivial. There is no nontrivial "precarious" phase for the3+ 1-dimensional sG model. The effective potential for the "autonomous" phase has asimilar form as the classical potential and the temperature effects only make contribution tothe infinitesimal part of this phase.
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