I have a 1 year old HP dv7 laptop with an Intel i7 quad core processor (1.86 GHz), 8 GB RAM and a 1 GB Radeon graphics card. Based on the requirements of TW2 and the specs of my PC, am I correct in saying that my computer should be able to run TW2 with no problem?

Yet every time I play TW2, My computer has to shut down due to overheating. I have very limited computer knowledge, but this, to me, raises a red flag. The only other game I have played on my computer is Icewind Dale, so I don't really have anything to compare this with to know if the problem is just TW2 or if my PC has some kind of internal problem. Any suggestions? Thanks, I appreciate it.

Also, when The game auto configures the graphics settings, it puts me on the lowest settings. Don't know if those two issues are related or not. Thanks again

This game is one of the most demanding (in terms of CPU and GPU load) ever. Since the harder you work the GPU, the more it heats up, it's not too surprising that it can cause some laptops (and even badly ventilated desktops) to overheat.

The dv7 is known for overheating. It's even been known to overheat playing WoW.

And since the 5650m, which is the usual GPU in the dv7, is below minimum requirements, configuring the game to low settings is correct.

It's a shame, but even some Alienware laptops (meant for gaming for crying out loud) cannot run at full capacity for a long time without overheating. First throttling occurs, which causes enourmous slowdowns and in extreme cases, the laptop will shut down.

If the laptop is known for overheating, there isn't much hope. What you could do is lower the speed manually (there are programs available to do this with ease). You could even modify your cooling system. I can understand fully if you don't want to disassemble your laptop, if it is even possible to modify or improve. I did it on my HP-mini 311c, where I put a small copper plate between cooler and cpu.
But it's quite an extreme measure :S