Das Feuer ist nicht kalt = the fire is not cold, nicht being not.
Das Feuer ist kein kalt = the fire is none/not any cold.
Saying the fire isn't any cold sounds really funny in english and might even be wrong. The fire is NOT cold, so nicht for not.
English UK native speaker.... think the English would be 'The ashes are not cold' ..... so they haven't been gone long, so we might catch up with them..... or possibly 'the campfire is not cold' so the scouts have not been gone long...