We study the three-dimensional fundamental-adjoint SU(2) lattice gauge theory at non-zero temperatures by Monte Carlo simulations. On an 8³ × 2 lattice, at β_A = 1.1, where β_A is the adjoint coupling, we find no evidence of any transition at the location of a previously known bulk phase transition around β = 1.33. Moreover, the deconfinement transition at β_A = 1.1 occurs at β = 1.20 and is of first order for β_A 1.1, thus implying a change of universality class from that of the Wilson action at β_A = 0. Computations of the plaquette susceptibility and the temporal and spatial Polyakov loops on 8³ × 4 and 16³ × 8 lattices at β_A = 1.1 further support these conclusions and suggest that the previously claimed bulk transition around β = 1.33 is, in fact, the first-order deconfinement transition. Simulations at larger β_A and the measurements of the mass gaps from the correlation functions of temporal and spatial Polyakov loops also confirm the temperature dependent nature of the above transition. The consequences of our results on universality are discussed.