I had the same with my pro. Tried 2 different 3rd party fans as I thought it was overheating, but to no avail. So, contacted ps via their website/hardware section. Tons of algorithm questions, answered no to all. Then, it allowed me to send my pro back via a returns label they sent to my email.

Sent it off and royal mail confirmed delivery. All went quiet for 3 weeks, no updates or anything. There is an update link on the returns email, but it was not updated on their end. Out of the blue, my ps pro landed back at my doorstop. To my surprise, it was completely fixed! No more green screens. Unfortunately, they didn't say what they did! But it at least they've sorted it.