Q: My sponsor has a model pic on their site that I think would be really great to use for promotion. Can I link to it or should I save it to my computer and serve it from my own site?

A: Neither.
If you link to it, then you'll be hotlinking -using someone else's image and bandwidth. If you just download it, then you'll be stealing. Email your sponsor and ask them about the image and if you can use it to promote their products. They may so no, but you won't know until you try. Most sponsors provide their affiliates with free content. Have you looked at the free content of your sponsor? Perhaps there is an image you can use from what's already available. I would also advise you that you ask before you do anything to free content imagery such as cut it up for graphics use.