She made her comments following a fire at the building on Tuesday night for the second night in a row.
Five fire appliances tackled the blaze which NIFRS said had been started deliberately by youths accessing the site of the former school.
Said Cllr Duffy: “After being contacted by local residents I went to the scene of the fire at the old school building on Tuesday night.
“There was a very extensive operation by the Fire Service underway to extinguish the fire and stop it spreading.
“These buildings have suffered from arson attacks in the past and I certainly hope this is not the start of copycat incidents.
“I would urge parents in the general Culmore area to advise their children to stay away from the old Thornhill school site.”