Statistically steady supersonic deflagrations are numerically investigated in narrow channels with strong thermal expansion and heat loss. Four modes of flame propagation are observed, namely, extinction, low-speed deflagration, high-speed deflagration, and DDT. It is determined that larger thermal expansion facilitates initiation of high-speed deflagrations while the heat loss can suppress the transition to detonation. The high-speed deflagration mode is shown to be the result of the dynamic balance between thermal expansion and wall heat loss. The limits of high-speed deflagration in terms of the thermal expansion and heat loss coefficients are determined. The statistically steady oscillatory high-speed deflagrations propagate at average velocities close to half of the CJ detonation velocity. The dynamics of the flame front and shock waves are visualized using numerical schlieren. Periodic acceleration and deceleration of the leading shock are identified, and the mechanism of DDT suppression is elucidated.