Effects of both finite temperature and density on Wilson line symmetry breaking mechanism is considered for an SU(N) theory defined on space-time manifold R1,d-2×S1 with massless fermion in the adjoint representation of the gauge group. Detailed analysis is given for the groups SU(2) and SU(3) on R1,2×S1. It is found that, at fixed fermion boundary condition, the critical temperatures and densities at which the full SU(N) symmetry is restored are the same for N=2 and N=3.