I'll use my case, but I think there is a lot of people in this situation.
My Mac Mini is 2007, 1.83GHz and now with 3GB of RAM and a Kingston SSD, running Lion. This combination provides satisfaction when working with web design, some publishing and daily taks. However, Safari is getting old and everything that uses graphics, specially 3D acceleration, is a problem.
Reading some articles around the web, it seams the only way out is to try the PCI port through Ethernet adaptor. In theory, might be possible to adapt a PCI connector (PCIe?) and connect external graphic card. In the real world, looking at my logic board, I don't think it's possible!
But recently I've seen some external cases for graphic cards that uses Thunderbolt port. So my new idea is to use the SATA port, a SATA-Thunderbolt adaptation (already exists) and a graphic card enclosure. This is not to get powerful graphics because the 1.5 GHz of Mac's SATA port will limit, but at list I'll be able to install newer OS with a simple hack, and newer graphic drivers.
What do you think about? Ideas?
I've never heard of an adapter that will let you convert a computer's SATA port to a Thunderbolt port. Thunderbolt is based on PCIe, and SATA is not (it uses controller chips that interface with PCIe, but SATA signaling is not the same as PCIe signaling). Do you have a link?
What you're looking to do has been done before, but with MacBooks. The AirPort card in MacBooks (and Mac minis) is PCIe-based. It's only a x1 lane width, but graphics cards will work. In fact, another member here has already done this with his own MacBook:
http://www.applefritter.com/content/gpu-upgraded-macbook-mountain-lion
Now, for the practical aspect: Your Mac mini is 8 years old. Brand new ones are $500. You're probably looking at dropping at least $200 to mod your current machine.
I could be wrong, but I think there is only Thunderbolt to SATA, not the other way around. If you've seen an adapter the other way, post a link, I'm curious to see what it would be.
I assume you could do the same thing with a Mac Mini, although you'd almost certainly need a longer cable than that. It's a fun project, but as mentioned, not practical. You can buy a used Mac Mini that will run Yosemite for $300 or less, or even a new one for just a little more, this would be far better in my opinion.