Can a 3D model of a copyrighted work be rendered legally without infringement? I know this is still gray territory and it is asked so many times within the 3D printing and maker community but I'm curious about the limits of 3D models and were it touches on Free Use and infringement. I'm not trying to push the envelope, I just want to be clear on the matter.

Is it legal if a design is rendered in a CAD program of a copyrighted material for no purpose of using, distributing, creating, mixing, internalizing, re-licensing under GPL/CC, or any unauthorized use outlined by the owner of the original work? For instance, if someone is demonstrating the abilities of a particular CAD and makes a mock-up of Mickey Mouse just to show the limits of said CAD and the STL/OBJ isn't released or distributed and a letter of intent is given along with the demonstration regarding the original work (in this case, Mickey), is that infringement? In this example, no loss of revenue or sales will affect the original owner, no claims of ownership is implied or stated, and no physical model will be created.

While considering all of this, I figured that it wasn't very much different than if an artist sat down and drew a picture of Mickey Mouse. As long as the picture isn't sold, distributed, or released, in my mind, that is the same thing as a 3D render.

To further the details of the 3D model, the render would be made from scratch and not imported, copied, or reverse engineered from any other work. Bottom line, it will be a likeness that is created but it will be as close to the real thing as possible to demonstrate capabilities of a particular program (such as organic shapes, stitching, grouping, layering, or any other facet and characterization of 3D modeling).

I already understand that it is recommended to err on the side of caution and steer clear of things like this but it is more of a curiosity than a request for legal advice regarding a specific case.

Can this be covered under Fair Use?

Since there is nothing to be made from creating the render, it isn't released or distributed to others, isn't re-licensed, and no ownership is implied/credit to the original owner is given, is this Free Use or copyright infringement?
First, copyright laws are complex and depend heavily on the specific details.  IMO, your question is really too broad to answer.

An interesting example of how details and interpretation affect whether something is a violation or not is Kienitz v Sconnie Nation.  In this case a copyrighted photo was clearly copied, modified, and used to make a t-shirt that was sold; but, it was not deemed a copyright violation.  On the surface it seems like a violation; but, the court ruled it was not a copyright violation because of the specific details of the case.  Using something as a starting point for a unique creative work that is clearly your own creation is not copying.  I am sure you can tell the difference.

Second, in your description you mention "Free Use".  If the owner has granted "Free Use" of their product; but, they are still wanting to declare the item copyrighted, I would hope that they have granted that "Free Use" under a defined agreement.  In that case, it would seem likely that the creator may just be trying to protect his design from being plagiarized and/or sold/used in a way that is against his intent.

If you have a way to contact the owner, why not just contact them and ask their permission for what you want to do.  If they have put it out for public use, they would probably be excited to have other people see their creation.  Just make sure they gets the credit for the design.  If it is a creation they are intending to protect (like Disney does with Mickey Mouse); then, the answer will be an unequivocal no.  Note that one weird exception is that Disney has granted use rights for Donald Duck to the University of Oregon "Ducks".

Finally, you state that that your intent is "for no purpose of using, distributing, creating, mixing, ..." and you list almost every way of making it public.  If your intent is for what you make/copy to never make it into the public domain; then, how will your question ever be anything other than hypothetical?  I know that there is presently no "private use" exclusion for copyrighted material.  It isn't legal to copy someone's DVD for you to watch privately; but, in reality, no one gets prosecuted for a single private instance.  It is abuse that gets prosecuted.

In what you intend, it would seem that you be best suited to seek out first what would be the "right" thing to do rather than just focusing on what would be "legal".  If you are concerned what you want to do may be wrong and/or illegal, it is probably best to not do it.