Wiktionary
lose their cool
vb. 1 (alternative form of lose one's cool English) 2 (en-third-person singularlose their cool)
Usage examples of "lose their cool".
To do this right they needed to give their detractors the chance to go berserk and lose their cool, to promise to take away their jobs and pensions, and to threaten them with prosecution, and they needed them do it all right in front of the president.