Hydrogen is regarded as a leading candidate for alternative future fuels. Solid oxide electrolyser cells (SOEC) may provide a cost-effective and green route to hydrogen production especially when coupled to a source of renewable electrical energy. Developing an understanding of the response of the SOEC stack to transient events that may occur during its operation with intermittent electricity input is essential before the realisation of this technology. In this paper, a one-dimensional (1D) dynamic model of a planar SOEC stack has been employed to study the dynamic behaviour of such an SOEC and the prospect for stack temperature control through variation of the air flow rate. Step changes in the average current density from 1.0 to 0.75, 0.5 and 0.2 A/cm have been imposed on the stacks, replicating the situation in which changes in the supply of input electrical energy are experienced, or the sudden switch-off of the stack. Such simulations have been performed both for open-loop and closed-loop cases. The stack temperature and cell voltage are decreased by step changes in the average current density. Without temperature control via variation of the air flow rate, a sudden fall of the temperature and the cell potential occurs during all the step changes in average current density. The temperature excursions between the initial and final steady states are observed to be reduced by the manipulation of the air flow rate. Provided that the change in the average current density does not result in a transition from exothermic to endothermic operation of the SOEC, the use of the air flow rate to maintain a constant steady-state temperature is found to be successful.