I always thought it had to be cold? You want the cold custard versus the hard shell of the sugar
Here is some text that "I think" was copied from Cooks Illustrated. The author writes likes this was a first attempt, yet her details are pretty specific. I've made the CI version before and it's just heavy cream and egg yolks, so I think this is it.
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When the ramekins are cool enough to handle, take them out of the pan and place on the wire rack. Allow to cool completely, about 2 hours. Transfer to a rimmed baking sheet and cover the baking sheet tightly with plastic wrap. Refrigerate for at least 4 hours, or up to 4 days.
Remove the plastic wrap. If any condensation collected on the custards, gently use a paper towel to soak it up. Sprinkle each dish with 1 to 1 1/2 teaspoons of turbinado sugar. Use a kitchen torch to caramelize the sugar. Refrigerate, uncovered, for 30-45 minutes (don’t let them sit longer than that) to re-chill before serving.