The most common and most likely answer to this crossword clue is the 7 letter word THAWING
I've seen this crossword clue in The Sunday Telegraph
T
H
A
W
I
N
G
More clues leading to the result THAWING
Buddy explains!
The straight part
We know that "sign of getting warmer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sign of getting warmer = thawing.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does THAWING mean?
THAWING verb- To gradually melt, dissolve, or become fluid; to soften from frozen
- To become so warm as to melt ice and snow — said in reference to the weather, and used impersonally.
- To grow gentle or genial.
- To gradually cause frozen things (such as earth, snow, ice) to melt, soften, or dissolve.
- The process by which something thaws.