Is it prohibited to blow on your food to make it cool down before eating or should we wait for it to cool down naturally, according to shari'a?
The scholars have consensus that blowing on food to cool it is makrooh (frowned upon) -in general- based on a hadith in Musnad Ahmad according to http://fatwa.islamweb.net/fatwa/index.php?page=showfatwa&Option=FatwaId&Id=2499 on the authority of ibn 'Abbas saying:
أن رسول الله صلى الله عليه وسلم نهى عن النفخ في الطعام والشراب
That the Prophet (ﷺ) prohibited blowing on the food and into the drink.
I found it also as quoted as a mursal of az-Zuhri in mosnaf ibn abi Shaybah (http://library.islamweb.net/newlibrary/display_book.php?idfrom=3332&idto=3332&bk_no=10&ID=3135 hadith #4).
Other evidences in Jami' at-Tirmidhi https://sunnah.com/tirmidhi/26/28 and Sunan abi Dawod https://sunnah.com/abudawud/27/54. Note that ibn abi Shaybah in the above link quoted 11 narrations and statements of scholars prohibiting or disliking blowing on food or drink or while praying and two narrations on scholars who don't seem to dislike it.
The reason for this ruling which was quoted by many scholars is that this is part of the good manners and virtuous as blowing on the food or in a drink may cause that one may spit on it or elave a bad taste (or odor) in the drink and this is certainly disliked. Also cooling food by blowing on it shows a lack of patience and haste which is disliked:
"Deliberateness is from Allah, and haste is from the Ash-shaitan." (Jami' at-Tirmdihi https://sunnah.com/tirmidhi/27/118 and also in bulugh al-Maraam https://sunnah.com/urn/2118260 where the weakness of this ahdith was addressed)
Note that scholars say if there's a necessity for this haste or eating the food as soon as possible it is permissible to cool it by blowing on it see also https://islamqa.info/ar/answers/100204/%D8%A7%D9%84%D9%86%D9%87%D9%8A-%D8%B9%D9%86-%D8%A7%D9%84%D8%AA%D9%86%D9%81%D8%B3-%D9%81%D9%8A-%D8%A7%D9%84%D8%A7%D9%86%D8%A7%D8%A1-%D9%87%D9%84-%D9%8A%D8%B4%D9%85%D9%84-%D9%85%D9%86-%D9%83%D8%A7%D9%86-%D9%84%D9%87-%D9%83%D8%A7%D8%B3-%D9%8A%D8%AE%D8%B5%D9%87