  We investigate the high temperature limit of SU(2) and SO(3) lattice gauge
theory, respectively. In particular, we study the Stefan-Boltzmann constant in
both cases. As is well known, the Stefan-Boltzmann constant extracted from
SU(2) lattice gauge theory by incorporating finite size effects is smaller than
the continuum value which assumes three gluon degrees of freedom. On the other
hand, the extrapolation of our SO(3) lattice data comes much closer to the
continuum value. This rises the question whether SU(2) and SO(3) lattice gauge
theories represent different quantum theories in the continuum limit.
