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I looked up あつい, and the top two results were different words with the same
pronunciation but similar though distinct meanings:

  * [熱い](https://jisho.org/word/%E7%86%B1%E3%81%84): hot, as in "stove"
  * [暑い](https://jisho.org/word/%E6%9A%91%E3%81%84): hot, as in "summer"

Do I understand correctly that these words are simultaneously heterographic
and synonymous? Wouldn't one be unable to convey the difference without
writing them down?
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2021-02-13T19:10:05.897
84187
2021-02-13T19:40:13.523
31850
question
words nuances
Which atsui do you mean?
They are heterographic as you say, but not synonymous. Since you already have
the meanings pretty much figured out, there is no need to go into detail. To
sum, 暑い describes weather/environment/temperatures, while 熱い describes
objects.

When you hear or see 「あつい」, context often determines which word is used.

The Venn diagram below, [copped from
Wikimedia](https://upload.wikimedia.org/wikipedia/commons/e/e7/Homograph_homophone_venn_diagram.png),
demonstrates several related concepts. To be considered synonyms, the words
have to have the same meaning but different pronunciations and spellings.
Strictly speaking "synonyms" exclude homophones and homographs.

「暑い」and「熱い」fall square in the purple area.

[![enter image description
here](https://i.stack.imgur.com/mLdvu.png)](https://i.stack.imgur.com/mLdvu.png)
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answer