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 29aMegillah 29a, based on Ezekiel 11:16Ezekiel 11:16).