C.M.
My son, now 18, has had his nose cauterized twice. The effect seem to last about 5 years. See an Ear Nose and Throat doctor.
Both heat and cold seem to trigger the nose bleeds, and if he gets one, he's likely to get another one (I think the scabs don't heal).
One doctor told me that I can put bacitracin or vasciline in his nostril to help the scab heal. (and limit the recurring bloody noses). I also make sure he gets a vitamin with iron in it because of the blood loss.
There is a product called "Nosebleeds QR" that I've got from drugstore.com (search on the internet). Someone told me it was used by boxers to stop nose bleeds. Its expensive - $5 or so for each application, but cheaper than a trip to the emergency room. (Once at middle school they called an ambulance when they couldn't get his nose to stop bleeding.)
Good Luck!