The question is, what's the purpose of this thread.
The question is: what's the purpose of this thread.
The question is: "what's the purpose of this thread".
The question is: "what's the purpose of this thread"?
The question is: "what's the purpose of this thread?"
The question is: "what's the purpose of this thread?".
I think the last one's correct: the sentence ends with a full stop because it's a statement, and the quote ends with a question mark because it's a question. Or is it even a quotation at all:
The question is: what's the purpose of this thread?.
Then...
Is the question, what's the purpose of this thread?
Is the question: what's the purpose of this thread?
Is the question: "what's the purpose of this thread"?
Is the question: "what's the purpose of this thread?"?
Is the question: what's the purpose of this thread??
?????