The thermo-acoustic oscillation (Taconis oscillation) in a two-dimensional (2D) closed tube with a large thermal gradient was studied by numerical simulation of the 2D compressible Navier–Stokes equations. Both ends of the tube were hot (T=TH), and the center of the side wall was cold (T=TC). We analyzed the stability of thermo-acoustic oscillations in the closed tube at various values of the initial pressure p0 and temperature ratio θ=TH/TC. Hysteresis phenomena were observed when the boundary layers are thin at the initial pressures 25, 35, 50, 75 and 100 kPa. On the other hand, we could not observe the hysteresis phenomenon when the boundary layer is thick at the initial pressure of 17.5 kPa. We analyzed the temperature distributions in the cold region, and a heat pumping from the cold region toward the hot region was observed in the cold region. These heat pumping phenomena are related to the hysteresis phenomena.