Human operators often experience large fluctuations in cognitive workload over seconds timescales that can lead to sub-optimal performance, ranging from overload to neglect. Adaptive automation could potentially address this issue, but to do so it needs to be aware of real-time changes in operators' spare cognitive capacity, so it can provide help in times of peak demand and take advantage of troughs to elicit operator engagement. However, it is unclear whether rapid changes in task demands are reflected in similarly rapid fluctuations in spare capacity, and if so what aspects of responses to those demands are predictive of the current level of spare capacity. We used the ISO standard detection response task (DRT) to measure cognitive workload approximately every 4 s in a demanding task requiring monitoring and refueling of a fleet of simulated unmanned aerial vehicles (UAVs). We showed that the DRT provided a valid measure that can detect differences in workload due to changes in the number of UAVs. We used cross-validation to assess whether measures related to task performance immediately preceding the DRT could predict detection performance as a proxy for cognitive workload. Although the simple occurrence of task events had weak predictive ability, composite measures that tapped operators' situational awareness with respect to fuel levels were much more effective. We conclude that cognitive workload does vary rapidly as a function of recent task events, and that real-time predictive models of operators' cognitive workload provide a potential avenue for automation to adapt without an ongoing need for intrusive workload measurements.