Why do recipes say to use eggs at room temperature?
Because temperature affects how eggs emulsify and incorporate air, and in baking those two properties determine texture more than almost anything else.
The main reasons:
Emulsification. Cake batters are emulsions — fat and water-based liquid held together. Cold eggs added to creamed butter cause the butter to seize and firm up, and the mixture curdles or splits, appearing grainy. A split batter traps less air and produces a denser, coarser crumb. Room-temperature eggs incorporate smoothly.
Whipping volume. Egg whites whip to greater volume at room temperature, because the proteins are more mobile and unfold more readily. This matters for meringues, soufflés and genoise sponges, where the air you beat in is the only leavening.
Even mixing and baking. Cold ingredients lower the overall batter temperature, which affects how quickly the cake sets in the oven and how the crumb develops.
Where it matters most and least:
Matters a lot: creamed butter cakes, meringues, whipped sponges, custards and anything relying on emulsion or aerated egg.
Matters little: scrambled eggs, most breads, brownies, and anything melted-butter based where the mixture is warm anyway.
For yolk emulsions such as mayonnaise and hollandaise, room temperature genuinely helps stability.
How to warm them quickly. Place whole eggs in their shells in a bowl of warm — not hot — water for five to ten minutes. This is far more practical than the standard advice to remove them an hour in advance, which nobody remembers to do.
Separating is easier cold, though — the yolk membrane is firmer and less likely to break. So separate straight from the fridge, then let the whites come up to temperature before whipping.
Food safety note: leaving eggs out for a short period is fine; several hours in a warm kitchen is not advisable.