We investigate the effect of putting a cutoff on finite-temperature field theory. We then apply this procedure to several currently interesting models, i.e., the Higgs model viewed as an effective low-energy theory, the Nambu-Jona-Lasinio model, and the dual superconducting model for the confining region of QCD. If the models predict a critical temperature well below the cutoff there is little effect from finite A. For T c close to A significant quantitative differences arise. We extend calculations on the phase transition in dual QCD and find a value of T c ≃ 200 MeV. By imposing a bootstrap condition, i.e., T c = Λ, we derive a deconfining transition temperature T c ≃ 325 MeV