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A fire crew from the Spreydon Station was sent to the park on the corner of Colombo and Brougham Sts at 3.27pm.
A Fire and Emergency New Zealand spokesman said the cause of smoke was a cooking appliance - which could have been a community barbecue or pizza oven.
He did not know what type of appliance was used or what was being cooked (or overcooked).
"They are all allowed, as long as they are not smoking out the neighbours too much."
But the spokesman said having a member of the public call the fire service is exactly what it wants people to do.
"That thing we are taught as kids - see smoke and call 111," he said.