Well, you can answer the valve question by simply doing a valve check/adjustment, so that’s easy.
I’m really puzzled about the overheating. Besides the cooling system causes that Jt105 mentioned, another thought I had is that engines burning lean mixtures run hotter. The lean burn would also explain the fluttering. But could possibly it run lean enough to overheat? That, I don’t know. What you could do is ride the bike awhile with the engine in the fluttering behavior, then stop, and pull the spark plugs and read their color. Are they stark white, like a lean burn? Are they both the same? They is a separate fuel injector for each cylinder.
Have you taken note if the gas mileage has changed since this problem arose?
Back on the idea about poor fuel delivery, it might also be worth the effort to measure the fuel rail pressure.