I also own an HP pavilion g6 laptop. I also had that overheating issue and very low battary lifetime issue with Ubuntu 13.04 and before. I solved both of those issues by simply turning off my discrete graphics card,i.e. AMD Radeon graphics card and leting ubuntu work with only intel card. You can do this as follows if you hope to use earlier version of ubuntu such as 13.04,12.10,12.04 so on and so forth.
chmod -R 705 /sys/kernel/debug
chown -R <your_username>:<your_username> #replace <your_username> with your username
echo OFF > /sys/kernel/debug/vgaswitcheroo/switch
And also I had to include the above 3rd command in /etc/rc.local file to turn the AMD card off at every startup.
But now, Ubuntu 13.10 supports Hybrid Graphics(AMD Radeon and intel HD graphics), means that you can now switch graphics between AMD radeon and Intel HD graphics as in windows. For this you need to install fglrx drivers as follows.
sudo apt-get install fglrx fglrx-pxpress
Reboot the system and you can start Catalyst Control Center either in dash or from terminal. To start in terminal, run the following command.
Remember to run this as root, otherwise you won't be able to switch graphics. And also, unlike in windows you need to reboot ubuntu after switching to make it work. I found this solution here, and it worked for me as crystal clear.
Hope this helps.