Given kept a cleansheet for the 1-0 win over Bolton Wanderers.
Given, who has also played for Newcastle and Sunderland, would not rule out extending his stay on Teesside.
He said: "It's great to be back in the North East, I spent so many years here. It's nice to complete the hat-trick at Middlesbrough.
"I was delighted to join. As soon as I got the call, I was straight up the A1."
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