The phrase "hot milk" refers to warm or hot cow's milk that has been heated, but not boiled. It is often used as a soothing drink before bedtime or to help with digestion.
Gradually whisk half of hot milk mixture into eggs, then whisk egg mixture back into milk mixture in saucepan. (epicurious.com)
Slowly pour hot milk into egg mixture, whisking constantly. (health.com)
When the entire 1/4 cup of hot milk mixture has been added to the eggs, slowly pour the egg mixture to the milk mixture in the saucepan, whisking constantly. (thegoodheartedwoman.com)