It happened that the volume of the content in the Program Files\Microsoft SQL Server\MSSQL.#\Reporting Services\RSTempFiles directory has grown over time and ultimately filled up the disk. Unlike SSRS logs (in the LogFiles directory), these temporary snapshots are not being cleaned up automatically. The "CleanupCycleMinutes"
In the interest of getting SSRS back online ASAP, we manually deleted the older snapshot files - reclaiming a decent chunk of space. Going forward, we will need to put in place a script or some sort to automatically and regularly keep the directory clean. Sounds like an action item.