  We have measured the correlation function of Polyakov loops on the lattice in
three dimensional SU(3) gauge theory near its finite temperature phase
transition. Using a new and powerful application of finite size scaling, we
furthermore extend the measurements of the critical couplings to considerably
larger values of the lattice sizes, both in the temperature and space
directions, than was investigated earlier in this theory. With the help of
these measurements we perform a detailed finite size scaling analysis, showing
that for the critical exponents of the two dimensional three state Potts model
the mass and the susceptibility fall on unique scaling curves. This strongly
supports the expectation that the gauge theory is in the same universality
class. The Nambu-Goto string model on the other hand predicts that the exponent
\nu has the mean field value, which is quite different from the value in the
abovementioned Potts model. Using our values of the critical couplings we also
determine the continuum limit of the value of the critical temperature in terms
of the square root of the zero temperature string tension. This value is very
near to the prediction of the Nambu-Goto string model in spite of the different
critical behaviour.
