Fake Christmas trees are made of synthetic materials such as plastic or metal, so they can indeed catch fire if they are exposed to high temperatures or if they are placed too close to a heat source. This is why it is important to follow all safety precautions when using a fake Christmas tree, such as keeping it away from heaters, fireplaces, or other sources of heat. It is also important to ensure that the tree is not overfilled with decorations, as this can increase the risk of fire.