Can all domain users be logged into one local profile?

I need to find a way to have all domain users log into a computer and all use the same local (could be temporary even) profile. In the end, I only want one folder under USERS and I DO NOT want roaming profiles to be used. Is this possible?

We need a bit more information to be able to fully answer your question, but here's a start:

Mandatory profiles force a given set of users to load a specific profile. When the user logs off, the profile is reset back to the mandatory profile saved. The standard process for assigning mandatory profiles does require that you store the profile on a server share and that you make some configuration changes to said domain users. This should work for you if you want this to apply to every machine the users log in to. If you only want it to apply when the users log in to a specific machine, edit your question to say so, and there are some other possible solutions.

As a side note, you may get better answers to this question on ServerFault, as this is more of an administration question.