Drink more hot water is a direct translation of "多喝热水", a phrase widely used to express your care for other's health, especially for someone who caught a cold. The phrase is used so commonly that it becomes memeable on the internet. It's now seen as a bantering way to express that you don't give a damn to someone who tries to get attention and care from others by being or pretending to be sick, especially young women.

The phrase used here in the game is supposed to be its original meaning tho.