On some days visitors to the Luigi Pigorini National Museum of Prehistory and Ethnography here may find its director in the front booth handing out entrance tickets. It’s not a meet-and-greet situation: The museum is chronically understaffed.

In recent weeks museumgoers have tended to speed past the glass-encased artifacts from Oceania and Asia or skim Homo’s evolution to sapiens. They can’t afford to tarry. The Pigorini has no money for air-conditioning, and the Roman sun is merciless.

“We barely have enough money to keep the lights on, or pay for a cleaning staff,” said Vito Lattanzi, director of educational services and of the Mediterranean collections at the museum, which is also a research institute. The custodial staff has been pared down to 11 from 30. Ten years ago there were eight to a shift; now there are four, and in most cases two are volunteers.

“We’re making a superhuman effort,” Mr. Lattanzi said. “We’re determined to keep the museum open, but the risk of a shutdown is there.”