If you didn't feel the case heat up, the thermal throttle never turned on.
It's one thing to speculate on why some are seeing browser performance issues on the M8 vs the M9 - it's quite another to go on a 810 witch hunt using repeatedly debunked myths vs facts.
I have on my M8 the very nice ViperOneM8 rom. Here's a screen shot of the notification pull down -
Notice that at the top, it shows how many cores are running and what the frequency is for each core.
You can pull that down by a few centimeters and watch what happens while the phone does things - like complex web page loads.
At no point during complex page loads is the processor running anywhere near hard or fast.
In fact, for those tasks, the M8 runs far below the wildest throttling speculations out there for the M9.
So attributing a browser slow down to throttling - when the M8 isn't running full on - is hereby debunked as well until someone posts core speeds with an M9 during tasking.
(Quick System Info PRO -
https://play.google.com/store/apps/details?id=org.uguess.android.sysinfo.pro - has a notification CPU cores frequency widget. No idea if it would work on the M9 but check if interested in repeating my test monitoring. Personally, I'd like to know.

)
The M8 - like the M9 - can and does peak all cores to full speed intermittently with any number of task combinations, including browsing.
No one here has reported thermal throttling. Please let it go.
The report here is that some things aren't responding properly.
Having beaten the throttling to death, let's try to find the real cause of any problems.