That's not actually evidence. I can't "just try it out", because I don't have a collection of flash games with html5 equivalents. And I still don't believe you.

Having my fans go on full blast because of Flash is something I remember happening quite often. Having my fans go on full blast because of html5 is not something I remember at all.

And your use of games here is a red herring. Nobody complained about games using up battery. The complaint was flash ads using up battery.