On the 1837 Ordnance Survey six-inch map it appears as 'Templefanum', a name suggesting ecclesiastical origins, the Latin 'fanum' referring to a sacred place or shrine. By the time the revised six-inch map was produced, the same rectangular, east-west aligned structure bore a second name alongside the first: Carpenterstown School. Whatever it once was, it had been repurposed.

The Ordnance Survey Field Name Books for County Westmeath, compiled in 1874, recorded that Carpenterstown National School was built in 1850 on the site of an ancient building known as Templefanum, understood locally to have been a chapel. The question of whether any fabric from that earlier structure survives inside the schoolhouse walls is genuinely unresolved. Render applied to both the interior and exterior surfaces obscures whatever stonework lies beneath, and no clearly medieval features are visible. The most notable architectural detail on the present building is a base batter on the west gable, a sloped thickening at the foot of a wall used to give it extra stability, here apparently functioning as a buttress against the rising ground on that side. It does not appear to be medieval in origin, and yellow brick is visible in its construction, a relatively modern material. About seventy metres to the south stands a seventeenth-century wayside cross, a small carved stone marker of the kind once placed at roadsides for the use of passing travellers.