According to Wikipedia’s infobox, apple pie may be served hot or cold. The choice is a matter of tradition and preference rather than a defining rule of the dessert.
Warm apple pie is often associated with freshly baked pastry and softened, fragrant apples. In the United States, it is commonly served à la mode, topped with vanilla ice cream, so the contrast between hot pie and cold ice cream becomes part of the experience. In Britain, custard is a traditional accompaniment, while whipped or poured cream is also popular.
Cold or room-temperature slices are equally ordinary, especially when the pie is being served later or sold in prepared portions. This serving temperature should not be confused with storage guidance: a baked pie may need to cool before cutting so its filling can set, even when the eventual serving is warm. The phrase “hot or cold” describes accepted serving styles, not a requirement that both temperatures be used.