Doesn't that sound good? :)
Download and burn an Ubuntu ISO, and stick it in the drive. Follow the prompts - it will always be a clean install when installing over Windows, just allocate all disk space to Ubuntu when prompted.
Generally, you can run quite a few Linux ISOs as a Live OS from CD or Flash before you install. Don't like the feel? Don't install it, and get a different distro, even a different Ubuntu (Kubuntu, Xubuntu - they have different desktop managers).
If you cannot use your optical drive at all, use the USB Flash drive method. http://www.pendrivelinux.com/create-a-ubuntu-9-10-live-usb-in-windows/
It is really just too easy. And Ubuntu has their own support Wiki and Forum for anything you might need.
edit: Hibernate is an iffy proposition with any OS, especially any OS that did not ship with the computer. Do not count on it to work any better in Ubuntu (but it might, who knows?).
If some of your problems are caused by heat, ensure the laptop is on a hard surface so it vents properly. You might also consider a good laptop cooler (Antec makes quality stuff, not sure about any others) http://www.google.com/search?ie=UTF-8&oe=utf-8&q=laptop+cooler .
Otherwise, you may have several independent components failing - optical drive, graphics card, whatever. I hope not. But if it overheats regularly, it is more likely things may start to fail.