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Not everyone in Christianity believes that the third temple will be built as a physical temple. Many believe the ginormous dimensions given for the temple in Ezekiel indicate that it is actually just a spiritual temple being referred to.
Some passages indicting that the view of the NT writers was that the third temple was spiritual are Acts 7:48 and surrounding, 1 Cor 3:16 and surrounding, and 1 Peter 2:5 and context. Mark 14:58 and similar passages that can be interpreted as being about the resurrection of Jesus' body can also be interpreted as being about the church as Christ's body, a "temple made without hands." See also Revelation 21:22.