What is the midrash about Nadav and Avihu being burned from within?

Question

In a recent study of the part of Sh'mini about Nadav and Avihu bringing aish zarah (alien fire), somebody vaguely recalled a midrash that the fire that killed them entered through their nostrils and burned them inside rather than them being engulfed in flames from outside as I'd always imagined the event. I found an article on the Chabad site that mentions this midrash and cites Tanchuma (nothing more specific). I tried searching Tanchuma (in English) on Sefaria but did not find this midrash. (I can work with a result in Hebrew but searching in Hebrew hasn't worked so well for me yet.)

Where can I find this midrash? I'd like to know what it says about what happened and also any conclusion it reaches about why it happened that way. (I have guesses about the latter but nothing I can support.)

Answer 1

Sanhedrin 52A (Sefaria)

בי אלעזר אמר אתיא שריפה שריפה מבני אהרן מה להלן שריפת נשמה וגוף קיים אף כאן שריפת נשמה וגוף קיים

Rabbi Elazar says that there is a different source for this method of burning: It is derived from a verbal analogy between the burning that is described in this context and the burning that is described with regard to the deaths of Nadav and Avihu, the sons of Aaron (see Leviticus 10:6). Just as there, Nadav and Avihu were killed by the burning of the soul, but the body remained intact, so too here, the execution is carried out by the burning of the soul, but the body remains intact.

ואידך ההוא שריפה ממש הואי ומאי דכתיב וימותו דאתחיל בהו מגואי כעין מיתה דתניא אבא יוסי בן דוסתאי אומר שני חוטין של אש יצאו מבית קודש הקדשים ונחלקו לארבע ונכנסו שנים בחוטמו של זה ושנים בחוטמו של זה ושרפום

The Gemara asks: And how does the other Sage, who does not derive that burning means this kind of death from here, interpret the death of the sons of Aaron? The Gemara answers: That burning was actual burning. And in that case, what is the meaning of that which is written: “And they died”? It means that the fire started from within them, and therefore it was similar to a natural death, which occurs within the person. As it is taught in a baraita: Abba Yosei ben Dostai says: Two threads of fire came out of the Holy of Holies and split into four, and two entered the nostrils of this one, and the other two entered the nostrils of that one, and the threads of fire burned them.

Answer 2

Midrash Tanhuma (Shemini, 12):

אלא יתברך שמו של מלך מלכי המלכים הקדוש ברוך הוא, שהוא עושה כמה נוראות וכמה נפלאות, ששלח האש כשני חוטין לכל אחד ואחד בחטמן ושרף את הנפשות, ובבשרם לא נגע ולא במלבושם, ויקרבו וישאם בכתנתם.

...He sent the fire like two strings to each and every one, in their nostrils, and burned their souls; but He did not touch their flesh nor their garments. "And they approached and carried them by their tunics." (Sefaria translation)