It is possible to boil water in an unwaxed paper cup without the cup igniting. Pour water or milk into the cup. Cut a small square of aluminum foil and place it under the cup. Set foil and cup in or on the hot coals. The foil protects the small lip on the bottom from burning. If flames rise against the top of the cup where liquid does not reach, the cup can burn.
You can also hard-cook eggs in a paper cup. It is also possible to heat a carton of milk if the carton is unwaxed. Open the milk carton top before heating.