During deepwater managed pressure drilling (MPD), the gas kick may occur in abnormally high-pressure formations. If the traditional well control method is adopted, the treatment time is long and the advantage of early gas kick detection of MPD is lost. The dynamic managed pressure well-control (MPWC) method can be used to rapidly treat gas kick in deepwater MPD. In this paper, considering the effect of large-variable-diameter annulus and complex wellbore temperature in deepwater drilling, a simplified model of non-isothermal gas–liquid two-phase flow was established for dynamic deepwater MPWC simulation. Using this model, the response characteristics of outlet flow and wellhead backpressure were investigated. The results indicated that the gas fraction, outlet liquid flow rate, pit gain and wellhead backpressure presented complex alternating characteristics when gas moved upwards in the wellbore due to the large-variable-diameter annulus. The outlet liquid flow rate would be lower than the inlet flow rate and the pit gain would decrease before the gas moved to the wellhead. The variation trend of the wellhead backpressure was consistent with that of the pit gain. When the gas–liquid mixture passed through the choke, the expansion or compression of the gas caused part of the choke pressure drop to be supplemented or unloaded, delaying the response rate of the wellhead backpressure. The wellbore temperature, borehole diameter and seawater depth had different effects on outlet flow rate, pit gain and wellhead backpressure. This research could provide a new idea for well control methods in deepwater managed pressure drilling.