The pair were teammates at Chelsea for three years between 2001 and 2004 under manager Claudio Ranieri.
Gronkjaer, the Danish winger, is remembered for scoring in the 2-0 victory over Liverpool on the final day of the 2002/03 season, which sealed Chelsea's place in Europe and convinced Roman Abramovich to buy the club.
That also happened to be Cole's best campaign at Chelsea, scoring six goals despite injury problems and a brief mid-season loan spell at Wolves.
Cole and Gronkjaer both played their part in Champions League qualification, but it seems the pressure of doing so took its toll on the two men.
Chelsea were facing financial oblivion at the time and the club's chief executive Trevor Birch actually addressed the team in the changing room before the Liverpool game to spell out the danger of losing the match.
Every game in the run-in was crucial, and Cole recalls losing his temper with Gronkjaer before a massive fixture.
"It was a heated training session," Cole said on the talkSPORT Breakfast. "We had a big game coming up on the weekend, and he just kept kneeing me in my back.
"It was annoying. I shouted, 'what are you doing?', but I was young so I was just taking it.
"The third or fourth time, I just turned around and I walloped him. It's not something I'm proud of, just something that was heat of the moment.
"When you're on the football pitch and you want to win the game and you've got this annoying character behind you, kneeing you in the back, you've got to do something about it - and I did!
"After that happened, I learned to restrain myself, because I realised how powerful I was."
Asked how Gronkjaer reacted, Cole recalls him laying motionless on the ground, sparking fears something serious had happened.
He added: "There was no reaction! He was out cold for a long time. I thought, 'What have I done?' I thought I'd killed him!"
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Former Chelsea striker Carlton Cole has revealed he once punched Blues teammate Jesper Gronkjaer and knocked him out cold in training.