I have a question about the point. I've read some books about a series of works for busy writers and other Deep POV, but I don't understand. The deep point of view is, for example, that's how it's depicted. (Bad example) Andrea's face turned red. (Good example) Heat is turned up. The point is that by describing the sensation of the character's inner feelings, not the external camera, the reader and the point-in-time character have a completely consistent experience. But I don't think there's even a word like 'her' for a successful deep point of view, but the example doesn't explain it this way. Why does her, his or her name continue to be used on the point? The reader's experience with the name mentioned does not seem to be entirely united with the character. If you know why, I hope you will kindly explain it.
When I can’t figure stuff like this out, I read, copy, or outline pages from a published book in the style I’m interested in. I don’t mean this to sound snarky. I only mean that sometimes these very academic questions are better understood by example. It seems like you have a very clear idea of your question, so I bet if you reread a few pages, the answer will jump out at you.
I think you're just looking at a grammar issue? To be grammatically correct, a sentence is "supposed" to have a subject. So we use pronouns or nouns for that purpose. In your example, you're using "heat" as the subject of the sentence, but really, this is pretty indirect from what you're actually talking about. I mean, the subject of the sentence in a non-grammatical sense is Andrea, right? Alternatively, you're looking at something very close to a passive voice construction, and while passive voice has its uses, I don't think it's too effective here. In your quest to remove Andrea from the sentence, you're kind of shifting the focus away from her. I guess there are different degrees of depth to a deep POV, but I don't think I've ever read any that go so deep as to erase pronouns or nouns. I'm trying to imagine a whole paragraph written like this, and it gets pretty awkward.
I agree that "Andrea's face turned red" is not deep POV--it's not even third person limited, because if we're inside Andrea, we can't see Andrea's face. However, I don't understand "Heat is turned up". My limited and/or deep rewrite of "Andrea's face turned red" would be something like, "Andrea's face was hot." or "Her face was hot." or something of the sort--something that goes to Andrea's sensations rather than how Andrea looks.
If you're deep POV you (the narrator) are basically in the character's head and you're seeing whatever they are seeing, feeling etc. That's exactly like firs person, only instead of "I" there's "he, she (or other pronouns of choice )" and names. Where first person would be (bad example but since we have to use pronouns... ) "I felt the heat go up" the deep third POV will go: "She felt the heat go up". If the character can't see something, including their own face, then you can't mention it. And while it's true that you should strive to cut down on names and pronouns, it's also good to keep in mind that they don't have to be completely avoided. "Heat is turned up" can be used in all sorts of POV, not just deep POV. That's more a matter of writing style. If every sentence begins with a pronoun or a name, it becomes really boring to read. It is a dark and stormy night. ChickenFreak wakes up, all sweaty and bothered. But it's not the weather to blame. The heat is turned up, there's no doubt about it. The darn air-con is malfunctioning again.
In deep third we often try to avoid the "filter words" like "she felt". So, assuming this was actually external heat, it might well be written as "the heat went up" or whatever. It's just weird here because I think it's meant to be internal heat, like her skin heating from embarrassment, but the decision to avoid pronouns makes that really unclear.
You can use names, but in deep third you are in the mind of the pov character so it would be rare Hammer picked up a ladle full of water and splashed it on the coals - I am in third and describing a scene from the outside The coals hissed and spat as Hammer tipped a ladle full of water over them (still in third); come on Hammer, you can take a bit of heat (but now in the characters head listening to their thoughts)
Third person is always describing from outside, only First is inside, technically. The only difference between your two examples is that the first is short and the second is more "writerly". "We often try to avoid" mostly happens when we are not trying hard enough to find an example where we don't avoid said expressions Because they do have their place.
I agree with your first statement with Andrea's face but I'm confused by 'the heat was turned up' I wouldn't class that as deep POV.
The fact that you are talking about the character as "he/she" and not "I" means exactly that the narrator is not the character, i.e. not an inside entity but an outside one. Of course in deep POV the narrator does have access to whatever's inside the character's head, they can see whatever the character sees but the narrator themselves is still an outside entity. Deep POV is like mindreading somebody else. It's still different than being in your own head.
It's different than being in your own head, just like first person is different from being in your own head (because a first person narrator is a character, not you). But you can be just as much in the character's head using third (or second) as using first. The difference between first person and third person is pronouns, not narrative distance.
Returning to offer an example: First person: The ground was wet, sopping under my fingertips. Joe had watered. And he’d weeded, in his usual sloppy way—the soil around the onions was torn up. So where was he? Kidnapped by aliens? I shouted, “Joe!” Third person: The ground was wet, sopping under her fingertips. Joe had watered. And he’d weeded, in his usual sloppy way—the soil around the onions was torn up. So where was he? Kidnapped by aliens? She shouted, “Joe!” Why is the first presumably “inside” while the second is presumably not?