The Temple was an extension of the concept of the Tabernacle which God instructed the Nation of Israel to build as a place for God to come and talk with them. That was the purpose of the Mercy seat, from which God talked to Moses.
The Temple was originally built by Solomon on the Temple Mount in Jerusalem, It was enlarged and enhanced by King Herod. It was and still is a revered part of Judaism, which is a point of contention with Islamist since they have built a Mosque on the site. According to the Jews that Temple must be rebuilt on the original plot where it was originally built.
That having been said; The most probable reason that the Temple is not used for Christian worship is because Gentiles are not allowed to enter past the outer part of the compound. This is vividly shown in Acts where Paul is accused of denigrating the Temple by bringing a Gentile into the Temple:
Acts 21:28 KJV Crying out, Men of Israel, help: This is the man, that teacheth all men every where against the people, and the law, and this place: and further brought Greeks also into the temple, and hath polluted this holy place.
There is only one Tabernacle and all that is currently left of it is the wailing wall.
The other places that the Jews congregated to worship were known as the Synagogue. These were in the Jewish communities. When Christianity began to spread due to the persecution by the Sanhedrin in Jerusalem, and elsewhere. 'The people of the way'; which was what the first Christians were called, began to meet in secret in homes in order to not be taken back to Jerusalem for punishment. Paul was on his way to Damascus to capture and take them to Jerusalem when He was converted.
Christians were persecuted by Rome until Constantine was converted, and during that period did not meet openly.