Not a single archeological remnant has been found of the Temple of Solomon; therefore, to describe it, we have to rely on two other sources. The primary source is the Bible, which supplies us with accurate descriptions and measurements (Kings I 6; 7, 14-15). The second source is archeological research from discoveries of that same time period found in the region.
We can assume that the architectural style of the edifice was drawn from regional influences. In fact, there is even an allusion to that in the Bible: And King Solomon sent and fetched Hiram of Tyre. He was the son of a widow of the tribe of Naphtali, and his father was a man of Tyre, a worker in brass; and he was filled with wisdom and understanding and skill to work all works in brass, and he came to King Solomon, and wrought all his work(Kings I 7;13-14).
Tel Ta'inat is a site in the north of Syria, where a long temple, with three internal divisions similar to the Courtyard, the Temple and the Sanctuary in the Temple of Solomon, was unearthed (Kings I 6;2-3,16). The Tel-Ta'inat site is from a slightly later time period than the Temple of Solomon.
Source: Israel Ministry of Foreign Affairs