Turn up the heat on someone
When you "turn up the heat" on someone, you increase the pressure on him or her.
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Today you heard that Trump was trying to turn up the heat on China with his recent moves against Huawei. When you are in a negotiation or a rivalry, you may want to increase the pressure on your adversary. If you increase the pressure on them, then you turn up the heat on them. Trump wanted to increase pressure on China (turn up the heat on them) with his latest move against Huawei.
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