I think the heart was required to help circulate blood through the brain, which was still dependent on organic material to function--In which case, I assume he still had a liver as well. I have to believe that the remaining organs still left in his body were simply the aspects of his humanity that they didn't have the facility to replace at the time. And Skynet, as well, probably just didn't have the technology to duplicate a fully developed human brain with all of its memories intact.
The only real problem I'm left with is how much those organs have aged prior to his revival. You have to wonder how long they'd stay potent.....unless they perfected cryogenics or...something.
