Which temple is being referred to in Acts 2:46? In the book of Acts, a certain temple seems to be being referred to in chapter 2 verse 46:


  Every day they continued to meet together in the temple courts.


Which temple is this?
The temple in Jerusalem was destroyed in AD 70. 

Acts 2 records how Holy Spirit was poured down on the Day of Pentecost (v 1-4). And then Peter addressed the crowd who were amazed and confused what was going on. Most of them were Jews who came to Jerusalem for the Pentecost festival (v 5). Following Peter's sermon, 3000 were baptized that day (v 41). From verse 42, the writer recorded the activities of the first believers. They devoted to the apostles’ teaching (v 42), they shared everything (v 44) and they met together in the temple courts everyday (v 46).

Acts 2 is no doubt before the destruction of the Temple in Jerusalem. Hence, it refers to the Temple in Jerusalem and none other.

What were they doing in the Temple courts? Meeting together and preaching about Jesus Christ as we see in the immediate next chapter, Acts 3, where Peter and John healed a lame man who was begging at the temple gate. 


  Acts 3:11 (NIV) While the man held on to Peter and John, all the people were astonished and came running to them in the place called
  Solomon’s Colonnade.


The believers  used to meet together in Solomon’s Colonnade, which was  on the eastern side of the temple.


  Acts 5:12 (NIV) The apostles performed many signs and wonders among the people. And all the believers used to meet together in Solomon’s
  Colonnade


You can see the picture of how the temple at that time looked like here in Wikipedia.