When you get offered a permanent job, generally they suggest that you don't hand your notice in until after all references and any health checks, CRB check etc are completed and your job offer is permanent. They'd then expect you to have to give a month's notice if you're already in a permanent job. This process can easily take 2 months or more - so there'd be a high chance that you would be able to finish your short term contract anyway. You would just tell them when they offered you the job that you wouldn't be able to start until the date you were available.
Plus, if you take the short term contract and then get offered the other job but they need you to start sooner, what have you got to lose - I mean, they can't stop you from leaving, even if you've said you'll stay, can they?
Just a thought...
Dave