Mooth breathing may not be soley becausevof adenoids it can be beacuse of blocked nose, large toungue other oral any deformities. Check for nasal block and deviated nasal septum with hypertrophy of turbinate inside nostril on one side this can cause moth breathing. Child is not willingly doing it so waring doesn't work, if nasla block is there give himregular steam inhalation twice a day, And see for other oral anamolies. If there is afamily history of hypothyroid get your child checked up thyroid levels once.