In use from 1910 until the 1950s, the power station has an impressive frontage, with opposing stone stairways leading to the front door. Inside, all is light and airy, with large windows and high ceilings. The floors are patterned with thousands of tiny ceramic tiles, and the original light fittings on cast iron sconces remain. Cast iron gratings and drain covers are stamped "SPQR", the municipal arm of the City of Rome. Ah, they don't build 'em like they used to.
The ground floor of the museum was the original basement, required for handling ash from the boilers above. Little remains of its heritage apart from rail tracks on the floor.
Glass cases around the room contain some of the museum's earliest exhibits including decorations found in Etruscan tombs and temples.
But it's the next floor up that provides one of those "OMG!" moments.
Two huge black engines lie there like the industrial monsters they were. At 8m long and 3m high, they dominate the room. Lined up alongside them, in almost comic relief, are hundreds of white and cream marble statues.
This juxtaposition of ancient and comparatively modern, of black and white, is astonishing.
The Centrale Montemartini has a permanent collection of 400 sculptures. They were moved to the site in 1997 while restructuring work was done on the Capitoline complex, a group of museums in the Piazza del Campidoglio on top of Capitoline Hill in Rome.
The exhibition was called, rather prosaically, "The Machines and the Gods", and was intended as a temporary measure. But when part of the collection was returned to the Campidoglio in 2005, it was decided to retain the old electricity works as a permanent home for recent acquisitions. Many of these were discovered during excavations between the late-19th century and the 1930s.
And what finds these were. Most are lifesize or larger, albeit with heads or limbs missing. In one corner of the room lies an enormous foot, about one metre long. Beside is a matching hand, and nearby the head. These are thought to be part of a devotional statue that would have stood 8m tall.
Pieces from Roman temples and triumphal arches are propped against the walls. Notable also are a terracotta statue of Athena and a beautiful marble statue of the muse Polimnia.
Next door to the engine room is the boiler room. The remaining coal-fired boiler, which was one of four, stands 10m high and 10m deep and three to four metres wide. It, too, is surrounded by sculptures and statues, which also flank the original control boards and switch panels.
As far as practicable, statuary found in the old industrial area has been incorporated into the exhibition, further strengthening the links between the ancient city and this example of industrial archaeology.
When you're fed up with the humdrum and banal (although it seems sacrilegious to describe Rome thus), try the Montemartini. Had the British had the flair and imagination of the Italians, perhaps the Tate Modern in London would look like this.
CHECKLIST
Getting there: Emirates flies daily into Rome from Dubai.
What to do: Visit the Museo Centrale Montemartini. Opening hours: Tuesday to Sunday 9am-7pm. Closed Mondays and some public holidays.
Phoebe Falconer paid her own way to Rome.