According to Wikipedia and the Jewish Encyclopedia, Reform Judaism, being originally opposed to the idea of Zionism1, called the Hamburg Synagogue "Tempel" to show that they no longer looked forward to the Third Temple in Jerusalem, and that individual, local, temples had taken its place. As DoubleAA points out, none of these sources offer conclusive proof that this was the original reason, however, they do point very strongly in this direction.
To quote the Jewish Encyclopedia
Reform conceives of the destiny of Israel as not bound up in the return to Palestine, and as not involving national political restoration under a Messianic king with the Temple rebuilt and the sacrificial service reinstituted.
Reform synagogues are generally called "temples" after the Hamburg, precedent, probably to indicate that they take the place of the temple in Jerusalem, which Orthodoxy looks forward to as the to-be-restored sanctuary.
Wikipedia (unsourced), in its article on the Third Temple, says:
Furthermore, there is a Reform view that the shul or synagogue is a modern Temple; hence, "Temple" appears in numerous congregation names in Reform Judaism. Indeed, the re-designation of the synagogue as "temple" was one of the hallmarks of early Reform in 19th century Germany, when Berlin was declared the new Jerusalem ...
And in Synagogues
The synagogue was renamed a "temple", to emphasize that the movement no longer looked forward to the rebuilding of the Temple in Jerusalem.
And in Temple
From the beginning of the nineteenth century, the word "temple" began to be used for Jewish houses of worship, almost exclusively by the followers of Reform Judaism, first in Germany, then in other countries, especially in the United States, as in Temple Beth-El. Orthodox Judaism considers this usage inappropriate, as it does not consider synagogues a replacement for the Temple in Jerusalem (there were local places of worship contemporaneous with the existence of the Temple, e.g. the one that can be seen at Masada).
1: In fact, many places online (including the Wikipedia article on the Third Temple) mention that an original Reform belief was that "Berlin was the New Jerusalem". I have been unable to chase the source of that idea down.