"deep warmth" is correct and usable in written English.
You can use it to describe an emotion or an atmosphere. For example, "She felt a deep warmth of peaceful contentment."
This set had begun with deep warmth; it ended with chords like icicles.
"Like most people across the house I have deep warmth and affection for Michael and resent unfair attacks upon him.
"Kim has this really deep warmth that you really empathise with her as a person through her characters".
"Eight Deadly Shots," with its all-encompassing humanism and a deep warmth of spirit despite the bleak circumstances it depicts, could not be more different from the contemporary TV shows to which MoMA would like to link it.
He was an outstanding supporter of many writers he knew, including myself, and I remember times with Ted and Seamus Heaney where the deep warmth of their friendship was palpable.
It is impossible for me to choose a "favourite" Chris image; the essence of the man, his humanity and deep warmth, always came through no matter how terrible the situation.
The hand-built Swedish-style hut may be well insulated, but if you feel yourself in need of a deeper warmth, the wood-fired sauna made from a converted horsebox down on the riverside should do the trick.
That approach works fairly well, but it's an incomplete subset of the broader and deeper warmth and competence perceptions that consumers unconsciously internalize.
It was a feeling, a deep spiritual warmth, I'd never experienced, living as I did, without a family, without a sense of belonging.
"Attempts by wicked people who tried to take advantage of our differences of opinion never affected his deep personal warmth towards me," Khamenei said in a statement.
Jane's dissatisfaction is magnificent – a deep hunger for warmth and love, but even more for truth and freedom.
