We study a phase transition in the Abelian Higgs model at finite temperature using the auxiliary mass method. We vary the gauge coupling constant q and the scalar self-coupling constant λ. We find that a first-order phase transition disappears at a tricritical point. It can be fit by the form q2~λζ very well. The value of the parameter ζ depends on the range of λ . Our results can be applied to experiments on high-temperature superconductors and liquid crystals. In particular, the tricritical point is κc=0.28 for superconductors, where q=2e.