Michael did not want to pursue the same lifestyle as his father and brothers. He was enroled in college and joined the army. Then based on the events of GFI he is thrust into the role as head of the Corleone family. This is something that he necessarily didn't want, but knows that he must do that thing to save the family.

The famous line in GFIII "Just when I thought I was out, they pull me back in" pretty much sums up Michael Corleone as a character. He is trying to not adapt the lifestyle of his father, but his efforts lead to events that make him a colder man.

In summary, Michael did not want to be Don, but realized it was necessary for the good of the family. I believe that partly explains the coldness of his character.