After much debugging, I was able to come to the conclusion that my specific case was related to a bug in the Oculus Rift software. Because the Rift, a virtual reality headset, requires low latency, their software seems to set the IDLEDISABLE power configuration to "1". In certain cases, after taking the headset off, the setting is not changed back to the default of "0".
IDLEDISABLE prevents the CPU from throttling itself, causing heat and the fan noise I observed. Additionally, this manifested in the Task Manager as "100% CPU usage". Process Explorer seems to always discount the System Idle Process and not include it in the total CPU usage, which is why it displayed a lower total CPU usage than Task Manager did.
To fix this, you can run the following two commands, which sets the IDLEDISABLE setting back to "0" and then re-applies the power management configuration.
C:\WINDOWS\system32>PowerCfg /SETACVALUEINDEX SCHEME_CURRENT SUB_PROCESSOR IDLEDISABLE 000
C:\WINDOWS\system32>PowerCfg /SETACTIVE SCHEME_CURRENT
A small note. Even if you don't have an Oculus Rift, the above could solve your problem.