Living systems sometimes experience abrupt tipping points in response to stress. Here we investigate the factors contributing to the appearance of such abrupt state transitions in animal societies. We first construct a mathematical account of how the personality compositions of societies could alter their propensity to shift from calm to violent states in response to thermal stress. To evaluate our model, we subjected experimental societies of the spider Anelosimus studiosus to heat stress. We demonstrate that both colony size and personality composition influence the timing of and recoverability from sudden transitions in social state. Groups composed of aggressive personalities transitioned into violent within-group dynamics sooner during heating, and also resisted recovery to baseline non-aggressive behaviour during cooling. We further observed hysteresis in groups composed of aggressive individuals, where group behaviour depended strongly on whether the colony had previously been in a calm or agitated state. These results demonstrate that a society’s susceptibility to sudden state shifts and their recoverability from them can be driven by the personalities of their constituents.