You must assume that if we have the technology to dig a hole through the center of the earth and out the other side, then we must also have the technology to make our tunnel air conditioned. So dont worry about the heat!
anyhow, the way i figure it, if you were to jump in, you would fall down, then up, then down untill you reached an equilibrium in the middle. If you are at the very center of the earth’s gravity will you float? will you stick to the sides of the tunnel like its a giant gravitron? i’d like to know your opinion.