Wolfe is the warden of Iron Heights Prison.
At some point in time he became the warden of Iron Heights Prison. Under his supervision a special cell was built for James Jesse in 2010 after he had talked his psychologist, who was visiting weekly into suicide. 
In 2015 Warden Wolfe took Joe West and Barry Allen to the cell of James Jesse, giving them necessary background information on the inmate, as well as a pack of licorice, which was needed to question Jesse. 
- Skilled psychologist: Warden Wolfe is seen knowing exactly how to treat James Jesse, building a special cell for him and using licorice to question him.
Behind the scenes
- In the comics Warden Gregory Wolfe is a warden at Iron Heights too, but he's also a meta-human with a power of psychokinesis, able to cause muscular spasm in people, or loosen the muscles - he uses ability in his work.
- In the comics Warden Wolfe is African American, while in the series he is portrayed as white.