Either a radeon rx7600 or a 4060. The lowest tier gpu's are usually the most power efficient. I'm sure you would see some performance gains as well but probably not an insane amount. But thats just the brand new gpus. You could get maybe a 6700xt which would have more vram than a 7600 for a bit more money.
To me it sounds like the problem lies with the titan x more than anything. Has it always had thermal issues? Could be a power supply issue or any number of things. I had a 2060 and my system was freezing for extended periods of times and eventually crashing my system and I assumed it was due to the summer heat. But I eventually replaced my psu and boom. No more issues.
Are you planning on using them as a pos? I'm not sure if an open pos os exists