It is shown how renormalization-group techniques which have been succe
ssfully applied to critical phenomena in condensed-matter systems can
be adapted to the study of phase transitions in field theories at fini
te temperature. Explicit calculations are described for the simplest c
ase of a self-interacting scalar field. A systematic method of estimat
ing the transition temperature to all orders of renormalized perturbat
ion theory is given, and the two-loop contribution is found. It appear
s, however, that there is an additional, non-perturbative contribution
which is not determined in the present work. An improved approximatio
n to the effective potential is obtained, in which the renormalization
group is used to resum the infrared singularities of perturbation the
ory. This shows that the transition is of second order. disproving rec
ent claims to the contrary. Gauge theories are discussed qualitatively
, While application of the techniques described in this paper will pro
bably show that the transitions in some gauge theories are of first or
der, it is argued that the order of these transitions can probably not
be detetermined reliably using methods currently available.