"great warmth" is a correct and usable phrase in written English. You can use it to describe a warm environment, a friendly relationship, or an emotional response. For example: "The crowd welcomed the speaker with great warmth."
"Really," Key persisted, with great warmth.
Contemporaries spoke of him with great warmth.
There are passages of great warmth and beauty.
A man of great warmth, charm and humor.
She brought great warmth & love to our congregation.
At his best, Hamilton's playing demonstrated great warmth and originality.
A person of great warmth, grace, kindness, and integrity, survived by wife Chandra, son Rajiv.
When she was finished, Rob took the tablet and smiled with great warmth.
All he touched will miss his great warmth, intelligence and creativity.
"She has a great warmth about her and a mercurial quality," he said of her Amanda.
Pausch talks about his students, friends and colleagues with great warmth and humour.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK