City host the Spanish giants in the first leg of the eagerly-anticipated last-four tie at the Etihad Stadium tonight having reached this round of the competition for the first time.
A fiery atmosphere is anticipated and City boss Pellegrini hopes his players have learned from their last-16 defeats to Barcelona in each of the past two seasons, when dismissals hampered their chances.
Pellegrini, a former Real coach, said: "Emotionally it is very important to have a hot heart but a cold mind
You can give an advantage to play with one player less, or commit an unnecessary penalty or things that decide the score.
"I think that is the lesson we must learn. It is important not to be emotional."
City will be without midfielder Yaya Toure for this first encounter and the Ivorian may also be doubtful for next week's return at the Bernabeu after suffering a thigh injury in Saturday's Barclays Premier League defeat of Stoke.
Captain Vincent Kompany is fit to start after being rested at the weekend and forward Kevin De Bruyne will also return after being given a game off.
Kompany has called on the City fans in a sell-out crowd to play their part.
The Belgian said: "I have never seen a Man City team not turn up when the fans are up for it. It is actually an appeal to them that they have to be as loud as they have ever been.
"Otherwise what is the point of buying a ticket to come in?"
Kompany, who recently returned from a month-long lay-off with a calf injury, also believes the occasion can inspire his team-mates.
The 30-year-old said: "When you get to the semi-final, there is nothing bad for you any more, you just want to play.
"For every single player in the team, if you are not hungry, you will never be hungry in football."
Source: PA