I have a character working in a short-term temporary position in an organisation and refer to her doing the work using the usual UK word, 'temping'. Will this be understood by readers in the US and other English-speaking cultures? If not, is there an equivalent culture-neutral term or should I spell it out?
I believe the word "temping" is culturally-specific, but not along national lines of culture. An American with experience in corporate environments where temps are common would know the word. A Brit without that corporate experience might not.
In either case, the word is pretty self-explanatory. I would use it without hesitation in anything I wrote.
All slang is culturally specific. The meaning of most of it can be figured out by context though. Certainly "temping" falls into that category.
But vocabulary recognition simply does not happen on a word by word basis. It happens in the context of the story being told. As kids, we pick up new words all the time, not from having them defined for us, but from hearing them used in context and seeing what they mean and how they are used. (This is why learning to speak a second language idiomatically from a book or in a classroom is so difficult. We don't get to see use in context.)
You can make up entirely new slang and just use it in context and if you set the context right, the reader will pick up its meaning.
Why not be safe? Explain the term the first time you use it. E.g.
Joan was working in a temporary position. She hated temping.
Something like this doesn't feel strange to those that know the word, and it helps those who don't.
The question, always, is who you write for. If you want to reach the widest possible audience, avoid jargon and slang, or explain it.
And, please, don't think that because a handful of other writers here on this site know or understand that word, the common reader will, too. If you want a useful answer to your question, you need to sample your target audience.
We have Temp Agencies in America, that, as their name implies, find temporary work for people. The people who work in temporary positions are referred to as "temps." I first heard the word in ordinary conversation when a friend referred to an acquaintance as a temp. So I recognized the verb "temping" immediately.
However, I'd never heard "temp" used as a verb, so out of curiosity, I did a google search to see if "temping" as a verb occurs in American English. Yes, it does. Here's an American article that came up: http://www.bestessaywriters.com/essay/the-temptations-of-temping/
I also found "temping" in this online American dictionary: http://www.macmillandictionary.com/us/dictionary/american/temp_2
(Underneath the definition, the user can click on "See the British English Definition", which in this case was the same as the American definition.)
So, I'd say you're safe to use it for your American readers. Perhaps you can do a country-specific search to determine if it exists in other English-speaking countries.