The 1983–1986 Pu'u ‘O’o eruption of Kilauea volcano had a very distinctive episodic character which later changed to steady-state activity. In this paper we present a physical model of episodic activity which explains the process largely in terms of non-uniform magma cooling and yield strength development resulting from variable dike width. The model is applied to the Pu'u ‘O’o data set and shows that, to explain the pressure variations within the summit magma reservoir and the patterns of summit deflation, a yield strength of 80 to 200 Pa needs to be developed. This corresponds to a temperature decrease in the magma of 10–15°C (consistent with temperature variations measured in the erupted lavas). The model stimulates the variation in volume flux as a function of time through the eruption and produces results which agree well with observed patterns of magma movement. Gradual evolution of the dike system through the eruptive series is explained by progressive widening of its narrowest sections. The loss of the episodic character and the transition to continuous activity is explained by a slight change in the thermal efficiency of the system. The change in pattern of gas release (from lava fountaining to gas pistoning and strombolian activity) which accompanied the change from episodic activity to steady-state eruption results from the reduction in magma flow rate at shallow levels in the dike system. However, we demonstrate that continuous eruptions do not inherently lack lava fountains — higher magma supply rates and thus higher flow velocities would allow fountaining to occur during continuous eruption. We demonstrate that episodic eruptions result from a fine balance between the effects of cooling of magma within the dike and the generation of pressure within the magma reservoir and thus that, thermally, episodic eruptions reflect a middle ground between short-lived fissure eruptions in which magma cooling dominates and continuous eruption in which cooling is minimised, the initial few months of an eruption being critical to establishing the thermal viability of the dike system.