Good news, everyone!  Through no effort of my own, the problem has gotten better.  Not gone away, but gotten better.
Oh, and I should have posted this earlier, but here are the specs.  It’s a laptop.  Is 6 years old but was top of the line when I got it.  Sooo, specs:
256 MB Nvidia GeForce Go 7900 GS
Dell Inspiron M1710 Intel Core2CPU @ 2.3GZ, 4GB RAM.
Windows Vista Home Premium 32-bit SP2
I am very suspicious of Flash, but Skype video-calls are bad too.  However, my Flash videos no longer pot out at 3 minutes.  All I did was give up and shut off the laptop for a bit.  Whiiiiiich reminds me that it was running awfully hot for a while.  It gets hot often, but I mean it was hot to the point where touching the back under the monitor or underneath was almost physically painful.
I downloaded Speedfan4.0.  As I suspected, the core CPU 1 and 2 temps aren’t changing, but the GPU is changing dramatically.
Upon boot, when everything is cold, it’s at 58.  Standard temp with no videos going is 72.  When I run Flash or a fullscreen skype video, it goes up to 77-78.  Maybe that’s normal, but maybe this whole issue has to do with the fans getting jammed up.
Anyway, let me follow Quartz’s suggestion and check out Task Manager while running a flash game.
Pre-Flash, Chrome is using 1 CPU and 200MB of Ram.  Now let’s play “Realm of the Mad God”
Ooooh boy.  Well it was flawless for the first 5 minutes, and the game is playing a lot better than it was before.  Now the relevant Chrome process is using 160MB of Ram and 60 CPU cycles.  Other Chrome processes have launched even though I only have 3 tabs open, like 8 or 9, using 600MB total.  It’s not the memory that worries so much as why it would take 60 CPU cycles.  And the GPU is at 74C.  Of course it’s possible it’s peculiar to this game.  Let’s try something simpler.
Angry Birds!  Well, this game is running smoothly with no slowdown, so hurray?  3 processes that seem related total 600MB of RAM usage and 50-60 CPU cycles.  Still a lot, but is not impairing gameplay.
Well, online videos are mostly back to normal, so I guess it’s just that one game?  Oh, and Skype calls still make the GPU run hot and the CPU cycles ramp up crazy.  Sooo, I still suspect there’s something funky with Flash, or that my GPU is old and/or clogged full of dirt.
What do y’all think?