の in traditional proper nouns are commonly written in katakana.
Practically, this can help people notice that this の is part of the proper noun and not the ordinary particle.
Historically, hiragana were not much preferred in proper nouns and official documents anyway. Meiji Constitution published in 1889 looked like this. (See: Orthography at the turn of the previous century) There were many katakana-only person names and place names in the old days. For the same reason, I would hardly expect hiragana in nameplates of real temples. Although this 火ノ寺 seems to be the name of a fictional temple, I can say this ノ adds an old and authentic look to the name.
It is a very difficult question even for Japanese.
I couldn't guess the reasonable reason why it was written as "火ノ寺" specially instead of the ordinary way as "火の寺", though の and ノ are interchangeable as is said in Tetsuya Yamamoto's comment for your question.
So at first, I thought that someone wrote it merely a choice to made their work stand out from other similar works; I know this is not a smart answer.
It turned out to be a proper noun appeared in The Naruto (Japanese: ナルト) manga and anime series that is a genre of ninja. In addition, there were other similar expressions using ノ instead of の like "木ノ葉 Ko-no-ha" and "木ノ葉丸 Ko-no-ha Maru", they were all proper nouns.
It happens that in naruto's answer there is a reasonable explanation that ノ are often used in traditional proper nouns, and I think it is a pretty promising answer. However, I considered the reason further.
If you are interested in knowing about ninja and know it well, I think that you know to call a woman ninja "くノ一 ku-no-ichi". When you break down a kanji character "女" into strokes, it will become "く, ノ and 一 ku, no and ichi".
I would like to think that ノ in "くノ一" inspired the author who considered the proper nouns in his managa like "火ノ寺 Hi-no-tera", "木ノ葉 Ko-no-ha" and "木ノ葉丸 Ko-no-ha Maru".