Remote assistance for highly automated vehicles involves a remote operator as a fallback whenever automated fleet vehicles require coordination and maneuver-based support. Similar to other control center professions, we expect that operator workload affects their attention and thereby their performance. To validate this, we conducted a simulator study to analyze operator workload under various task load conditions using a remote assistance dashboard mock-up. We used a within-participants design varying task frequency and task complexity for a set of scenarios generated from a previously defined remote operation scenario catalog. Our findings indicate that high workload through high task frequency and high task complexity results in longer task completion times and more errors when resolving a task. Additionally, low task frequency leads to longer task initiation times after a break. Combining high complexity and low frequency task load leads to the worst performance across multiple metrics, indicating an out-of-the-loop performance problem when low task frequency does not provide a sufficient base-load for complex tasks. Finally, we collected and analyzed physiological data from an electrocardiogram and an electro-dermal activity sensor to find stable indicators of workload changes across study participants. We find that heart rate and heart rate variability show significant differences when task frequency is modulated. In addition, the number of skin conductance response (SCR) peaks and the SCR half-recovery time vary significantly with task complexity. These results provide evidence that we are able to identify workload changes using physiological indicators in time-critical scenarios as basis to provide state-based support to operators when needed.