turn the heat on someone or something
turn the heat on (someone or something)
1. To pressure someone to do something. We need to turn the heat on those guys so that they finally pay their debt to us.
2. To start to do something or compete against someone with more determination or intensity. Wow, they really turned the heat on their opponents after halftime—the score went from 0-3 to 15-3 in less than half an hour!