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I noticed that dictionaries usually treat differently some homonyms, which for
a learner's perspective look similar. For example:

  * 熱い and 暑い are usually two different entries
  * 早い and 速い are usually one entry, shown with multiple kanji. Even though 早い and 速い have a different usage.

To me, both fit in the "very similar in meaning but used in different
contexts" category. For comparison, I find it logical to have two entries for
熱い and 厚い and one entry for 青い and 蒼い.

As a learner I see little difference between the two examples. Is there a
fundamental difference between these pairs of homonyms, is there something
deeper, maybe from the etymology?

If so, is it important for a learner to see those two cases differently?
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question
homophonic-kanji dictionary homonyms
Is there a fundamental difference between homonyms with close meaning and words with multiple possible kanji?
The short answer is no. The semantic "distance" between two homophones is
determined at the discretion of the authors of each dictionary, and it is
impossible to draw an official line. Some dictionaries may define 鳴く and 泣く in
one entry, while others may define them in two separate entries.

Etymology is an important criterion, of course, but how much emphasis is
placed on it depends on the policy of the dictionary. A dictionary that
focuses too much on etymology may not necessarily be handy for everyday use by
modern speakers.

Nevertheless, I agree most dictionaries explain 青い and 蒼い in the same entry,
but 熱い and 厚い in separate entries.

**EDIT:**

Word | _Meikyō_ | _Daijisen_ | _Kōjien_  
---|---|---|---  
**あつい** | **3** [暑][熱][厚] | **3** [暑][熱][厚] | **2** [暑/熱][厚]  
**はやい** | **1** [早/速/疾/捷] | **1** [早/速/疾/捷] | **1** [早/速/疾/捷]  
**つとめる** | **3** [務][努][勤] | **3** [務][努][勤] | **1** [務][努][勤]  
**なく** | **2** [泣][鳴] | **1** [泣/鳴] | **1** [泣/鳴]  
**あおい** | **1** [青/蒼] | **1** [青/蒼] | **1** [青/蒼]  
  
As for あつい, _Meikyō_ and _Daijisen_ define 熱い, 暑い and 厚い in three different
entries, which is perfectly understandable to me. _Kōjien_ defines 熱い and 暑い
under the same entry, which is perfectly understandable, too. As for はやい, all
the three dictionaries I checked define 早い, 速い (and 疾い, 捷い) in one big entry,
but _Meikyō_ explains when to use which kanji in detail.

Basically, you won't know until you actually look it up in each dictionary. We
can only guess, but _Meikyō_ is a relatively small dictionary designed to
provide practical explanations for learners of modern Japanese, so they may
have thought 暑い and 熱い are different enough practically. _Kōjien_ is an
authoritative large dictionary with lots of trivial or obsolete definitions,
and they may have thought 暑い and 熱い are the same word etymologically.
_Daijisen_ is somewhere between the other two. Ultimately, it's up to the
policy of each dictionary.
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answer