The most common and most likely answer to this crossword clue is the 7 letter word WARMING
I've seen this crossword clue in Independent
W
A
R
M
I
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G
More clues leading to the result WARMING
Buddy explains!

The straight part
We know that "heating up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case heating up = warming.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 WARMING mean?
WARMING verb- To make or keep warm.
- To become warm, to heat up.
- To favour increasingly.
- To become ardent or animated.
- To make engaged or earnest; to interest; to engage; to excite ardor or zeal in; to enliven.
- To beat or spank.
- A small rise in temperature.
- A beating; a thrashing.