Why does Reform typically call it a Temple, vs a Beit Knesset, a Beit Sefer, or a shul? I imagine the Hebrew would have been the obvious go to, if they chose to ignore the yiddush.
Not that I know the origin of Shul, I assume Yiddish in some form, but not sure what the original word is.
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.
And
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.
There are 876 Reform congregations in North America, 499 of which have "Temple" in their names, so the formal name is pretty common and it's not unreasonable to think that people refer to the others as "temples" too. As noted by DoubleAA, the first (apparent) use of the name was the Hamburg synagogue in 1818. Documentation about naming practices that early is hard to come by, but we might find hints in the official "platforms" published by the Reform movement (as it formed into an actual movement).
The first of these, from 1885, explains their views on Zionism and messianism:
We recognize, in the modern era of universal culture of heart and intellect, the approaching of the realization of Israel's great Messianic hope for the establishment of the kingdom of truth, justice, and peace among all men. We consider ourselves no longer a nation, but a religious community, and therefore expect neither a return to Palestine, nor a sacrificial worship under the sons of Aaron, nor the restoration of any of the laws concerning the Jewish state. [...] We are convinced of the utmost necessity of preserving the historical identity with our great past.
Perhaps the combination of "we're not anticipating a third temple" and "historical identity is important" led to the name being considered appropriate. Nearly a century later, the 1976 platform said:
We are privileged to live in an extraordinary time, one in which a third Jewish commonwealth has been established in our people's ancient homeland. We are bound to that land and to the newly reborn State of Israel by innumerable religious and ethnic ties. [...] At the same time that we consider the State of Israel vital to the welfare of Judaism everywhere, we reaffirm the mandate of our tradition to create strong Jewish communities wherever we live. A genuine Jewish life is possible in any land, each community developing its own particular character and determining its Jewish responsibilities. The foundation of Jewish community life is the synagogue. It leads us beyond itself to cooperate with other Jews, to share their concerns, and to assume leadership in communal affairs.
The temple was the center of Jewish life in biblical times. The Reform movement does not seek a third temple but believes that such centers of life are necessary everywhere that Jews live, and also that maintaining a connection with our national history and land is important. One way to do that is to refer to those local centers as "temples".
The short answer is: we don't know. The word Temple was first introduced in the title of the organazation which drove to found the Hamburg Temple: The New Isaelite Temple Association of Hamburg, a group of 66 layman (not the leading Reform Rabbis of the time) which arranged for the opening of the Hamburg Temple in 1818.
You can read in The Jew in the Modern World: A Documentary Reader (Mendez-Flohr and Reinharz, Oxford Univ. Press. 1995. page 161 link) parts of the constitution of that Temple, and while they are open about certain ideological and practical reforms they are making, they don't openly discuss their choice of names. To quote the first footnote to that text:
Some historians see an idological motive...behind the Reformers' naming their synagogue a "temple." That is, that by adopting the designation traditionally reserved for the fallen Temple of Jerusalem, the Reformers symbolically relinquished the hope of Israel's restoration and declared Hamburg their Jerusalem. Other historians ascribe to the Refomers the more innocent motive of simply wishing to distinguish their house of worship from the traditional synagogue of Hamburg.
Certainly this fact was used by the Orthodox as something to complain about, but it's worth noting both that the initial Reformers' weren't as extreme as their followers became, and additionally synagogues have been traditionally identified as the modern analogue of the Temple as far back as the Talmud (Megillah 29a, based on Ezekiel 11:16).
