  We obtain the effective potential at finite temperature within the left-right
symmetric model. We take the Higgs sector to consist of two doublets and
calculate its finite temperature effective potential up to the order of
``ring-diagrams'', using analogous techniques to those employed in the
derivation of the effective potential in the Standard Model. We find that two
first order phase transitions can exist, one at the $SU(2)_R$ breaking scale,
the other at the usual $SU(2)_L\otimes U(1)_Y$ breaking scale. Even though more
parameters are present than the standard model, we find that the electroweak
phase transition is still too weak to allow baryon asymmetry to survive the
transition, if the lower bound of the Higgs boson mass from experiment is
adhered to.
