Temp job etiquette

Recently, I started a temporary position with no solid end date--basically work until your assignment is completed. In this situation, would I continue to interview as normal and let them know that I may not be available for a month? Would it acceptable to give a two weeks in this kind of position? Or do I stick this out and not bother with interviews until my assignment is either complete or near complete.

I'm basically just converting old paper records to digital if that helps. I've never had had a temp job in my life so I'm not really sure what's expected of me here.

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