The exchange could be heard from the stump microphones.
As the crowd booed the Kiwi, Warner was heard saying: "C'mon mate".
Southee then explained: "He (Burns) was out (of his crease)".
Warner shot back: "But you hit his hand".
Southee shrugged it off: " Well he was in front of the wicket".
It only angered Warner more.
"C'mon, you're supposed to be Mr Nice Guy," Warner said.
Former Aussie captain Ricky Ponting said it was clear from the heated exchange that the battle will rage during this series.
"I tell you what the Aussies will notice - there was no apology, either," Ponting told Channel 7.
"He didn't say sorry at all."
Kiwi legend Brendon McCullum defended Southee, by suggesting his throw slipped from his fingers and he didn't intend to strike Burns.
"I think it's gone horribly wrong, I think it's caught in his fingers," McCullum said.
"David Warner didn't miss him anyway."