Here is part one of Story Sensei’s article on third person deep (limited) PoV. Check it out. Well written. Direct. Topical.

Story Sensei has a great blog for writers.

‘Deep Point of View, part one

The point of going deeper in your limited third person point of view is to stick the reader in your character’s skin. This will often result in a more powerful emotional experience for your reader.
There are some tips to follow that pull the reader deeper into the character’s point of view. Often a judicious word choice does the trick for you without changing the text.
These things will work to pull the reader into the story world and experience the story through the character’s eyes, in the character’s body. It usually gives more intensity to the reading flow.
Eliminate emotion words.
Many times, when a writer names an emotion, it distances the reader from the character. For example:

Anxiety trembled in her stomach.
Anger coursed through her.
She shivered as fear tiptoed down her spine.

It’s not that it’s wrong to name the emotion—in fact, sometimes it makes the sentence more powerful—but many times, when you rewrite the sentence without naming the emotion, the vision evoked in the reader’s mind is more emotionally impactful.
Ultimately, you want the reader to feel the emotion with the character, and readers don’t often feel the emotion when they read the words anxiety, anger, fear, etc.
They feel the emotion when they’re in the character’s body and head, feeling the physical sensations, acting with the character, thinking their thoughts, speaking their words.

An electric mixer in her stomach scrambled her insides.
Her body went rigid and her clawed hands trembled, a thread away from ripping the smile off his face.
A ghostly fingertip drew down her spine, freezing her shoulder blades together.

As with anything, moderation is the key—if the sentence flows better and is more powerful by naming the emotion, there’s no rule that says you can’t do it.

via Story Sensei: Deep Point of View, part one.’