A lattice computer simulation of a symmetric A-B-A triblock copolymer melt is reported. This melt is quenched, in simulation, from an athermal state to 39 different temperatures using cooperative motion algorithm. Energy, specific heat, copolymer end-to-end distance, bridging fraction, lamellar spacing, concentration profiles, and microstructure visualizations are reported. The quenching simulation results are compared with those obtained by alternative thermal treatments, that is by slow heating and slow cooling. Quenches yield data consistent with theory and experiment, whereas slow cooling and slow heating results do not capture the expected behavior for the lamellar spacing and the bridging fraction. Finally, at very low temperatures, below the conventional order-disorder transition temperature, an additional ordering is recorded, from a conventional lamellar phase to a lamellar structure showing copolymer junction points condensed into a two-dimensional plane. (C) 2003 American Institute of Physics.