In September, Wolf ordered the state to provide sex-reassignment surgery, saying it is the only way to treat Kosilek's "serious medical need."
Kosilek was born male but has received hormone treatments and now lives as a woman in an all-male prison. Kosilek was named Robert when convicted in the 1990 murder of wife Cheryl Kosilek.
In his ruling, Wolf noted that Kosilek's gender-identity disorder has caused Kosilek so much anguish that she has twice tried to commit suicide. Wolf said Kosilek "continues to suffer intense mental anguish" because she truly believes she is a woman trapped in a man's body.
"That anguish alone constitutes a serious medical need," Wolf wrote.
The Department of Correction has appealed Wolf's order.
The judge also heard arguments Monday on the department's request to put the order on hold while the appeal is pending.
Kosilek's lawyers also asked Wolf to revise his ruling to change his use of male pronouns to female pronouns when referring to Kosilek. Wolf said he would consider the request.