There were no flames or smoke and the fault did not damage the building or the part of the computer system it was supposed to help protect.
Even so, the building was evacuated about 8.30am, until the Fire Service gave the all clear about an hour later, customer services general manager Grant Strang said.
The council's telephone service was diverted to its after-hours service until about 10am, and the council's core computer systems were not fully operational until about 10.30am.
Mr Strang said staff were evacuated after a "battery acid-type, cable-burning" smell, noticed about 8.15am in the third floor computer server room, intensified.
The fire service responded and used heat and gas-sensing equipment to determine nothing was burned and that the air was not flammable, Mr Strang said.
The smell was from a bank of batteries in the backup power supply to the so-called core switch, which allows all parts of the council's computer network to communicate, Mr Strang said.
The pack had "started to cook itself".
It had overheated, its plastic faces had started to melt, and its vent caps had popped to release the pent-up gas inside.
The pack was immediately withdrawn and the core switch was connected to a 40kVA unit, which meant the battery pack would not have to be replaced.
Mr Strang said there were no reports of data being corrupted or lost during the well-managed computer shutdown.
The files were backed up, and there had been no power failure.
Analysts and technical staff would report on the incident.
