  We examine certain issues related to the universality of the SU(2) lattice
gauge theory at non-zero temperatures. Using Monte Carlo simulations and strong
coupling expansions, we study the behavior of the deconfinement transition in
an extended coupling plane (beta, beta_A) around the tricritical point where
the deconfinement transition changes from second to first order. Our numerical
results on N_tau =2,4,6,8 lattices show that the tricritical point first moves
down towards the Wilson axis and and then moves slowly upwards, if at all, as
the lattice spacing is reduced. Lattices with very large N_tau seem to be
therefore necessary for the mixed action to exhibit the critical exponents of
the three dimensional Ising model for positive values of the adjoint coupling.
