Good find!
Keep in mind just swapping the thermostat still leaves the radiator heat exchanger as part of the 10r80 cooling loop, so some of that heat and load will still be put in the 10r80 fluid/cooling system. Not a bad thing for warm up on a street driven car, potentially not a great thing for track/performance cooling.
Few thoughts:
1. How to deal with hard lines going to and from the OEM thermostat?
2. Need dimensions and threads/connectors in/out of OEM thermostat for fitment?
3. Full size improved racing thermostat or compact model?
Might be an few hundred dollar experiment, but you could buy a spare OEM thermostat and buy the improved racing thermostat(compact version?) and compare measured dimensions to see if the fit is close enough. This is including finding out the proper threads, or adapters needed.
You are more likely to be better off cutting the OEM hard lines on one or both directions towards the thermostat, and using a hard line to AN adapter. I used a hard line to AN adapter, and then an AN to push lock adapter, then I put a rubber hose over the push lock and clamped down with constant tension spring clamp. I used push lock and constant tension spring clamps at each end of my custom rubber lines, especially since my trans cooler used push lock already. This allowed me the flexibility to have whatever size improved racing thermostat and to mount it where/how I wanted.
Depending on the length of the replacement AN lines, going with AN fittings may not make sense or allow the flexibility you would need. You can reference my 10r80 custom cooling thread to see how I cut the hard lines and converted to AN and push lock to rubber lines. For how short my custom cooler lines were going to be, it didn't make sense to use AN fittings and PTFE/nylon tubing.
Here are more reference links:
OEM S650 10r80 thermostat BT4Z-7H322-B: https://parts.levittownfordparts.co...67qwvo6HK8NyPbHbj1og6Hck9-nqQJbGpTD2jZBIKupEC
Full size Improved racing trans thermostat I used: https://www.improvedracing.com/high-flow-engine-transmission-oil-cooler-thermostat.html
Compact size improved racing trans thermostat: https://www.improvedracing.com/compact-high-flow-engine-transmission-oil-cooler-thermostat.html
