I originally bought this off gamersgate and while I could get it to run with acceptable framerate, etc, the game would make my GPU overheat in minutes, even though more graphically intensive games did not have this problem. I brought this problem up at the 1CC forums but got no response and the Armored Princess demo had the same problem.
According to this threat at Quarter to Three, I wasn't alone in having this problem:
http://www.quartertothree.com/game-talk/showthread.php?t=51295
So did GOG manage to fix it? It looks like a fun game, but not fun enough to risk breaking my computer.

The same problem here. nVidia 9600GT...

Was this roughly... 1-3 months ago or so? maybe a bit longer...
Nvidia had a faulty driver that resulted in overheating GPUs. they rolled it back pretty quickly, but anyone who upgraded in that time window ran the risk over overheating... a few people had the worst happen, as you can imagine. They've since replaced the driver with an updated one that doesn't have this problem. Could have been the problem.
*Edit* reading the thread linked in the OP I see now that this was a problem that predated the Nvidia driver problem.

So, umm...Is this game "safe to play" then? Does the overheating problem concern both laptops and desktops?

I didn't have any problems so far...

Well i dont have overheat problems.And the game doesnt crash a single time on my wn7.
Also, there are such things like zalman coolers.They are top quality and they a definately a worthy upgrade(at summertime), if you are living in a hot country..
But i guess these troubling thoughs come only to those who has notebooks..so i have no idea.

It bears repeating: played other games on the exact same setup, many of them more graphically impressive, none of them had the sudden and acute overheating problem of KB, never played another game since with that same problem.

I never had that issue on two different Nvidia cards so, I guess I can't help you, other than potentially showing it's not a widespread issue but it only occurs on certain setups, for God knows what reason. Have you tried making sure vsync and all similar features are on (keeping in mind some such features may not work in windowed mode)? Some games don't have frame rate limiters, so if you have vsync off, they run at like, the max possible FPS, 100-500-1000 or whatever they can, which obviously can make a card work its ass off even if it doesn't need to in order to run the game well, which could lead to overheating. I got that with a simple Squaresoft game that's like Puzzle Quest, with mostly static 2D backgrounds and stuff, yet as soon as I started it up I heard the GPU's fan spin up to max speed, since it had no frame rate limiter. Sadly vsync also didn't work with it so I ended up not playing the game. Oh well. Anyway, I hope you can play this game.

Please write your computer spec. (dxdiag better).
Both of you, who doesn't have problems, and who does have problem.
And send it to support and post it here.

Been playing the Steam version, and in 10+ hours of gameplay so far had one hard system freeze which looked like it might have been caused by overheating. Monitored temperature for an hour after that and the GTS 250's core temp never rose above 73C (most games top out at 72, only a couple I've seen get it to 74). If this happens again I might manually put the fan to 100% when playing it.

Overheating may be caused by AA. But mind my use of the word "may" here. Disabling AA fixed the overheating problems on our desktops (single & dual 8800GTX), but it made no difference on a friend's ATI (forgot the model) desktop.
Incidentally, Fantasy Wars and, I think, Elven Legacy, both have a similar issue which also may go away if you disable AA.
I believe menu sluggishness is entirely fixable by forcing KB:TL to use a single CPU core. Google how (even if you already know, because there's free apps with nice GUIs out there to do it for you, and if you play old games it will not be the last time you need to do this).

Update:
Turns out the problem was an issue with the Nvidia drivers:
http://www.fuyoh.net/2010/06/22/kings-bounty-the-legend-hot-as-hell/
For some reason Dell just never bothered updating their official Nvidia drivers for my model laptop. If I was the paranoid type, I'd say they did that on purpose to speed my aging laptop to its grave in hopes of return business. Installing the latest drivers right off Nvidia's site fixed the problem.

I had the same problem, SpeedFan showed I was running 70 degrees C. I fixed it by replacing the stock cooling on the Graphics Card (Nvidia GeForce 7900 GT). I got the "ARCTIC COOLING Accelero" for about thirty bucks off newegg.

Now it runs in the high 30s, low 40s. I was shocked that it actually worked. Check the reviews on this. It just barely fit in my case.

I for one give up on this buggy game. Keeps overheating. Uninstalling!

I really want to play this game but my laptop gets really hot. After my computer turned itself off because of overheating I´m to scared to try again.