I have a third hand Q3 with a TW0J and a 2 stage tailcap. I run the MP 3.7V-4.2V cells from AW in it and nothing has fried yet. I get about 40-45 minutes runtime and it is considerably brighter than on a primary cell. As of a few days ago, I've run each cell (I have two) through 10 runs on the Q3 and everything is working fine.
As mentioned, the light gets warmer than on primary cells but even if you put in a fresh cell, turn the light on (on high, of course) and let it run on a table for 20 minutes, it never gets too warm to pick up. I also wanted to check into if it might be hurting the circuitry (by heat) so I ran the light for about 15 minutes and took it apart as quickly as I could (maybe 45 seconds) and the circuit board wasn't appreciably warm. Better heatsinking would be nice (wouldn't it always?) but the outside of the light gets warm indicating that stock heatsinking isn't quite terrible.
As far as voltage damage to the star itself, my theory (and my theory is equally worthless as the others put forth here
) is that the star is significantly underdriven using the stock circuit (about ~400 - ~550 mA) that with the extra voltage the star is likely being driven at close to spec or a bit overspec. But I have several lights that run completely direct on various LiON cells. I'm sure that the star won't last as long if you always run it on a 3.7-4.2V LiON but then, it's only a $30 light... If already have an LiON charger and you buy two LiON cells for $6 each, you've already justified the use of LiONs vs $1.25 each primary cells after 10 battery changes, discounting the fact that your Q3 is maybe twice as bright as on pirmaries. So if you have to swap out the star with another $10-$15 part, you're still quite a bit ahead of the $$$ curve.