In an interview on CBS News' The Early Show, Hensley's brother Ty said his family has been on an emotional roller coaster since Jack and two other workers were abducted from their walled-in residence in a Baghdad neighborhood Sept. 16.
All three were civil engineers working for General Supplies and Commercial Services, based in the United Arab Emirates.
Confirmation that the body found Wednesday was Jack Hensley's came after his brother was interviewed. However, Ty Hensley appeared to be braced for the news. "I've had one moment thinking there is an ounce of hope and doing all I can do. And another moment, like there is no hope but still doing all I can do," he told co-anchor Harry Smith. "I can tell you now, that these people no longer have control over my emotions and that I'm managing them on my own and they cannot impact them anymore. So there is some clarity on that."
The news came a day after a posting on an Islamic Web site said that an al Qaeda-linked group in Iraq had slain a second American, presumably Hensley. The claim came a day after the group said it beheaded fellow U.S. hostage Eugene Armstrong.
Ty Hensley said his brother, whose 49th birthday is Wednesday, went to Iraq in the first week of March. "And his reason for going was he wanted to make some money for his family, just to keep the bills paid," Ty said, referring to his brother's wife and daughter in Georgia.
Jack had worked on the water supply and the utility grid and was working on rebuilding a museum. While he was aware of the danger, he thought his work on behalf of the Iraqi people and his respect toward them would be appreciated.
"He knew if he laid low and kept quiet, they did not - they just respectfully lived their lives quietly over there, that he felt that that's what he would do," Ty said.
He described his brother as a "a great writer," and said he last heard from him on Sept. 13, just days before his kidnapping. "He answered questions for my kids, who, you know, want to know about the kids in school over there, things like that."
Letters home indicated how risky his situation was becoming, Ty said. In correspondence with his wife, he said, Jack had "mentioned that they're having a hard time keeping guards and that one of the guards actually told them that he would be killed if he came to work there and was warned."
To the Iraqi kidnappers, Ty said, "This will be felt with my family for generations. Grandchildren who are not born now are going to know about this and are going to be hearing about this. The world, this will come and go in a day or two. The cause for these people is, you know, for them to kill innocent people, they were shown that this was an innocent person and they still wish to kill him."
Tawhid and Jihad, Arabic for "Monotheism and Holy War," has claimed responsibility for the slaying of at least six hostages in the past as well as these kidnappings. The group is linked to suicide car bombings and coordinated gun attacks against U.S.-led coalition forces, Iraqi security and politicians and Iraqi Shiites. It has demanded the release of all Iraqi women in prison. The United States says only two women are being held and has refused to release them.
"They asked for people who didn't exist," Ty said of the militants. "And they made no way to contact, they made no efforts to contact any embassy. The United Nations did nothing. Why couldn't they have done something? They want to get in the middle. Isn't this a good time to get in the middle?"
Ty thanked Americans for their support, saying the family's phones were worn out. "I'm just a regular person. I don't have the capacity to handle a thousand phone calls an hour," he said, thanking Smith for the opportunity to "get out the story that his life mattered."