[en] We compute the leading and next-to-leading corrections to the finite-temperature scalar potential for a (3+1)-dimensional φ⁴ theory using a systematic 1/N expansion. Our approach automatically avoids problems assoicated with infrared divergences in ordinary perturbation theory in h. The leading-order result does not admit a first-order phase transition. The subleading result shows that the exact theory can admit at best only a very weak first-order phase transition. For N=4 and weak scalar coupling we find that T₁, the temperature at which tunneling from the origin may begin in the case of a first-order transition, must be less than about 0.5 percent larger than T₂, the temperature at which the origin changes from being a local minimum to being a local maximum. We compare our results to the effective potential found from a sum of daisy graphs. (orig.)