Setting up temporary e-mail with a different doman name

How can I set up a temporary e-mail address that would go to my regular email, but with a different domain name.....

Lots of registrars will allow you to forward email from a domain name you registered with them to another email address. That would be the cheapest way (if you have this service available to you).

Unless you need a specific domain, just get a gmail account.

Oh, if that's the case, I can also suggest Sneakemail.

That's a cool little tool. Thanks for that.