Vehicles and other items complicated the efforts to contain the fumes, as four crews arrived on the scene.
CCTV footage show smoke coming from a car in the workshop, quickly followed by flames underneath the vehicle.
TFS said in a statement it "started from an overheating engine compartment in a car that was being stored in the building".
"The engine compartment of a car caught fire a short time after it was driven into the workshop, and the fire quickly spread to the rest of the building, fuelled by gas cylinders, cars, and workshop and building materials," said Regional Fire Investigator, Station Officer Adam Doran.
"Fire crews contained the fire to the school's trade training centre building and were successful in stopping it from spreading to other parts of the school, with the added support of Hobart Fire Brigade's new aerial firefighting platform."
The damage and cost of the fire is projected to be in the multi-millions range.
Officer Doran said "thankfully, no one was in the building when the fire started, and no one was injured".
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