"I'd like to see him, if he'll come out with the same aggression as last Test, if he will do it as captain," Warner said.
Kohli took over Mahendra Singh Dhoni, who announced a shock retirement from Test cricket.
"MS (Dhoni) thinks a lot about the game, he's very knowledgeable, He knows how to go about getting each individual out. You can see the plans and you know what they're going to bring to the table. In that way he's a very, very smart captain.
The opener said it remains to be seen what Kohli brings to the table.
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"And Virat straight away had two players back which is the thing we use - to mix up the batsman's feet and have him thinking the short ball is coming then try and get them playing forward. The way Kohli is and goes about the game he's a fiery character but he goes out there and plays with his heart on his sleeve," he said.
"I wouldn't say crossing the line, but I've been guilty of it sometimes in the past. Just the way we celebrate wickets, not just the Indian team, we do it as well. Sometimes we've all got to be careful not to get overexcited and get in the batsman's face.