I don't see a stylistic disconnect between the style of the towers and steeples and the rest of the building. The overall style is fairly consistent with English Georgian architecture of the mid-18th century. The Temple would not have looked out of place stylistically if it had been constructed in 18th-century London. St. Martin's in the Field comes to mind since it employs some similar architectural elements -- but there are other examples of English Georgian architecture that are even closer in style. However, the proportions, shape, and usage of the Temple might have been quite jarring if it had been constructed back then. I don't think anyone would have dared to put a steeple -- let alone two steeples -- on a building that resembles a government building or palace more than a church.
Nevertheless, I don't think that supersupper is necessarily incorrect in calling the style of the building (minus the steeples) "Beaux Art." That architecture style, which was popular in the late 19th and early 20th centuries, used classical elements in a similar manner, as taught in the academies, but based more on 18th-century French models rather than English.