In that case I think I'd avoid saying 'Next Thursday' at all, and instead use either 'This Thursday' (the day after tomorrow) or 'Thursday Week' (seven days after that).
I think 'last May' is ambiguous from June to about now-ish. 'This May' will mean May 2012 until January 2013, unless clarified with '-coming' or '-past'.
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On the other hand, "Thursday after next" might actually be a week after this Thursday.
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I think 'last May' is ambiguous from June to about now-ish. 'This May' will mean May 2012 until January 2013, unless clarified with '-coming' or '-past'.