Temperature of Broth for Gravy

When making gravy, should the broth added to the roux be hot?

Roux, a mixture of flour and fat, is used to thicken gravy. After the roux has cooked for a few minutes into a paste, broth is gradually whisked in. It used to be said that the broth must be cold or the gravy will turn out lumpy. We made three gravies, one with gently simmering broth, one with room-temperature broth, and one with cold broth. Adding the warm broth shaved a few minutes off the cooking time, but there was no discernible difference in quality. Do, however, add the liquid gradually, whisk consistently, and always whisk out any lumps before adding more liquid.

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