The most common and most likely answer to this crossword clue is the 11 letter word TEMPERATURE
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More clues leading to the result TEMPERATURE
Buddy explains!

The straight part
We know that "a degree of warmth" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a degree of warmth = temperature.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 TEMPERATURE mean?
TEMPERATURE noun- A measure of cold or heat, often measurable with a thermometer.
- An elevated body temperature, as present in fever and many illnesses.
- A property of macroscopic amounts of matter that serves to gauge the average intensity of the random actual motions of the individually mobile particulate constituents. http//arxiv.org/pdf/physics/0004055
- The state or condition of being tempered or moderated.
- The balance of humours in the body, or one's character or outlook as considered determined from this; temperament.