This is just my opinion (feel free to contradict or add to this!)
A tuned NT is the best carb for stock engines. Realistically and theoretically speaking, the so called "HP" or cheap "upgrade" carburetors do nothing to increase HP. Honestly there should be more info for beginners warning them not to use these rip off carbs. They're worthless.
I don't give a crap about temperature for these MB engines. Bikeberry keeps spreading this false rumor that you need a cool down period after 20 or 30 mins of riding. Lol the people at Bikeberry are the dumbest people I've ever seen, all they can do is sell you boost bottles and banana "expansion" pipes and "high performance" colorful Chinese junk. That's complete BS. I rode my
stock MB for 3 hours and 30 minutes straight once, full throttle with no breaks on a 44T so i was hitting 9K RPM the entire time and it was 91 degrees outside. That thing got as hot as it could ever get. Stock exhaust as well which definitely does not help cool the engine due to its restrictive nature. Opened up engine afterwards, no damage at all. Cylinder and jug looked great. Compression test, exact same PSI. Later I was experimenting with carb jetting and ran the bike (still stock) FAR too lean (barely running) for two hours on a hot day. And the same for the next few days. Same story, no damage to jug/piston, engine great inside. That engine now has 600 miles on it and runs to this day, although I've scrapped it due to bolts stripping and clutch issues.
So if I were you I wouldn't be afraid to go lean. Sounds like you're a too lean right now however with the NT or you have an air leak. That #66 may be a bit too small. Try a #67 or #68 and see if you get a linear throttle response with it. It's all about patience at the margin with tuning carbs. I personally hate tuning carbs but the gain is worth it.
also, water should boil if you drip it onto your exhaust pipe...no such thing as an internal combustion exhaust below 220F!