Pentecost Not at the Temple?

I've always thought that in Acts 2, when Peter and the others were filled with the Holy Spirit on the day of Pentecost, and Peter preached the first sermon, that all this took place in the Temple. But just now I've read the first few chapters of Acts specifically asking that question, and I'm surprised to find that the text indicates that it took place at the disciples' "hotel", not in the Temple.