coin a phrase,
it means to invent a new saying or idiomatic expression that is new or unique.

Although not a literal translation, this could work, as it expresses the same notion.
"We are not exaggerating if we say that despite his apparently cold physical mood, the artist... must be painting at high temperature."
Or (pax Marcelo):
"If we say that despite his apparently cold physical expression, the artist, ...must be painting at high temperature, it is no mere wordplay.

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Note added at 4 hrs (2020-02-04 19:58:15 GMT)
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I'd have more trouble translating "sin que se advierta" and "talante" in that paragraph.

A metaphor is a figure of speech that describe an object or action that isn't literally true, but helps explain an idea or make a comparison.

It's all from context, and I would use overstate the case myself.
These options reference coin a phrase and exaggerate but are more subtle/subliminal to me.
Agree that coin a phrase does mean invent a new one.
Come up with a phrase is more finding the right one (and you can change phrase to term/word, description, metaphor or whatever fits best the hot/cold comparison the author sets up) so it doesn't have to be new.
Overstate the case means you're not going too far in asserting or using this analogy/comparison/whatever. It's one step pulled back from exaggerate.
I would use overstate the case, but a lot depends on your style and the tone you've established in your translation...

Describing his fever-pitch work pace with a cold disposition, and later using 'temperatura alta'

Possible translation:

"From the [very] beginning, Del Petro works feverishly. No play on words [or sort of pun] intended but despite his seemingly cold predisposition, the artist, without noticing, must have been painting while [quite literally] running a high temperature/fever"

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Note added at 3 hrs (2020-02-04 18:58:18 GMT)
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As for the suggestion of 'to coin,' I don't see what could be coined (o acuñado).

Rather than inventing a new phrase, s/he appears to be using/playing with contrasting terms (fever, cold, and high temperature) to describe the artist and his work ethic??

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Note added at 9 hrs (2020-02-05 00:56:19 GMT)
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Correction: 'must be painting' (and not 'must have been')

Another, more slightly literal option:

From the start, del Prete works at a fever pitch. If we say that, despite the artist's seemingly cold nature, he, without noticing, must be painting with a high temperature, we mean not to simply turn a phrase/create a sort of play on words. He works a lot, day and night, and tears up [destroys] almost everything he produces

at a fever pitch (idiom)
https://dictionary.cambridge.org/dictionary/english/fever-pi...

sin que se advierta = without noticing
su talante físico aparentemente frío = his seemingly cold (physical) nature

hacer una frase = turn a phrase/create sort of a play on words

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Note added at 2 days 9 hrs (2020-02-07 01:16:12 GMT)
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Through the use of 'frio,' 'temperatura alta,' and 'intensidad febril,' with the latter easily rendered as 'feverishly' or 'at a fever pitch,' the author appears to be engaging in a sort of a play on words, as s/he very cleverly expresses a contrast between the artist's *cold* demeanor and the *feverish* intensity of his work habits, hence my suggestions.

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Note added at 2 days 9 hrs (2020-02-07 01:36:35 GMT)
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Perhaps the idiom 'to turn a phrase,' which I added at the 9-hour mark, may also be an especially good option.

"...we do not intend to (simply) turn a phrase..."

"turn a phrase" (idiom)
To express something in very adept, elegant, and clever terms.
https://idioms.thefreedictionary.com/turn a phrase

I hope this helps! Cheers from Vietnam :-)