According to Numbers 19:2, “a red heifer without defect” was required for the ritual of purification.
An organisation called The Temple Institute is committed to searching for a red heifer without blemish as part of its preparations for the construction of a new temple in Jerusalem. The Temple Institute previously claimed in 1997 and again in 2002 that a red heifer without blemish had been born, but in each case it was later decided that the heifer was unsuitable. In March 2010 The Temple Institute announced that it had found a suitable heifer.
On the Temple Mount currently sit the Al Aqsa Mosque and the Dome of the Rock, which are regarded as holy by Muslims. These would need to be removed before a Jewish temple could be constructed, so the aim of orthodox Jews to restore the Temple heighten tensions between Judaism and Islam.
For Christians, Jesus is the final sacrifice slain “outside the camp” (Hebrews 13:11-13) like the red heifers under the Law. There is no need for further sacrifice.
Some Christians have claimed that Jesus will not return until a new temple is build on the Temple Mount but this claim is disputed.