Crossword Genius

Problem solver when things heat up (6)

Ross

I believe the answer is:

summer

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'heat up' is the definition.
Although both the answer and definition are verbs in their base form, I don't understand how they can define each other.

'problem solver when' is the wordplay.
'problem' becomes 'sum' (arithmetic problem).
'solver when' becomes 'mer' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'sum'+'mer'='SUMMER'

'things' is the link.

Can you help me to learn more?

(Other definitions for summer that I've seen before include "Warm season, allegedly" , "year" , "Period of heat" , "Beam" , "See 10" .)

I've seen this clue in The Independent.
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