Should I have my permanent or temporary address on my W2?

Your W-4 is just for the employer so they will withhold the amount of taxes you want withheld.  It does not dictate anything regarding how you file your actual tax return.  It is not clear whether you will need to file a MN state tax return.

You have referred to both your W-2 and your W-4 in your question.  They are different documents.  A W-2 is the document you will receive from the employer in January that details all of your earnings and the amounts withheld for taxes, Social Security, Medicare, etc.  Your W-2 has the information that has to be entered on your tax return.  You will want to make sure that it has an address that is correct so you will receive it from the employer in January.