When hiring a temporary employee do you have to specify the expected end date of employment to make the employment relationship contractual instead of at-will?

No. You can absolutely specify both an anticipated end date for the employment relationship and that the employment is at-will, and I would recommend communicating both in the offer letter. That way there’s no confusion about the nature of the relationship, and it’s clear that employment will most likely conclude at the expected end date and that neither the employer nor employee is bound by contract to finish out the assignment.

Content courtesy of the HR Support Center – https://affiliatedpayroll.myhrsupportcenter.com