My laptop is almost identical to yours and installing the standard Catalyst drivers did not fix the problems with the fan and temperatures. (In fact, it caused a new problem of booting into low graphics mode.)
This is because the Catalyst drivers currently have problems with the switchable graphics. The problems with the fan and temperatures were fixed only after following the instructions at: Workaround for Radeon Switchable Graphics in the Ubuntu Community Documentation.
Here are the instructions:
1) First open a terminal window. You can use ctrl + alt + t
2) Then copy and paste the following commands one at a time into the terminal. Press Enter after each command. To paste into a terminal window, right click and use the paste command from the context menu or click the mouse wheel or middle button. (Note that ctrl + v will not work.)
sudo apt-get purge fglrx*
sudo add-apt-repository ppa:andrikos/ppa
sudo apt-get update
sudo apt-get -y upgrade
sudo apt-get --reinstall install xserver-xorg-video-intel
sudo apt-get -y install fglrx-updates fglrx-amdcccle-updates
sudo aticonfig --initial -f
3) After the first command, you will be prompted for your password.
4) When you are finished, you will need to reboot.
As an aside, it's apparently common for the brightness controls to not work out of the box with HP DV6. If you find this is the case on your laptop, see:
Brightness not working on HP DV6