While looking around, I found this [湯冷ましを兼ねて] expression that no dictionary
has been able to translate.

Examples of use would be the [再び湯冷ましを兼ねて周辺を徘徊。] line in [this
post](http://redsnowman.cocolog-nifty.com/urawa_goten/2009/07/post-a4f8.html)
or the first sentence in [this
tweet](https://twitter.com/nbcnbnc/status/295542916850524160), just picking up
two random google results.
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question
translation
What does "湯冷ましを兼ねて" mean?
The expression ～を兼ねて means "combined with ～", or simply "with".

湯冷ましを兼ねて（何かをする・どこかへ行く）means "to do something/to go somewhere in order to cool
down after a hot bath".  
It has been questioned in comments to an earlier version of this answer
whether the purposive interpretation of "in order to" is adequate. While I
don't think that it would be adequate to translate every instance of を兼ねて as
"in order to", it appears to me that in this instance, i.e. 湯冷ましを兼ねて, the
action of cooling down after a bath is what one wants to primarily achieve.
The action expressed by the matrix predicate is the one that one sees as
suitable of achieving this purpose. The relationship between the two actions
can then be expressed by purposive "in order to".
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answer
[湯]{ゆ}[冷]{ざ}まし is one word. It means cooling down your body after taking a
bath. In our culture, the bath tub is significantly important in daily life,
compared with other countries. I think it's because of the damp weather in our
archipelago.

When parents see their kids staying naked and watching TV after bath,
especially in winter, they may say "湯冷めすると風邪をひくから、早く服を着なさい。". It means 'Wear
something now because you will get a cold if you cool down too much."

This "冷まし" is attributive form of "冷ます", "冷め" is a nominalization of verb
"冷める".

Both verbs mean cool down, but "冷ます" is transitive, and "冷める" is intransitive.

Good example is "[目]{め}[覚]{ざ}まし時計" = alarm clock (clock that _wakes_ you), and
"目覚め" = awakening (you _wake_ up).
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answer