Dealing with a faulty dGPU in a Pavilion 6100?

I have a Sandy Bridge based HP Pavilion 6100 which worked OK for around 4.5 years (well, the hard drive died, but I was going to buy an SSD anyway). Unfortunately, today Windows failed to start multiple times. I have a dual-boot installation so I tried Fedora instead. Fedora complained about the Radeon (a 6770M) card not responding for around 10-15 seconds, but eventually booted more or less normally (I never use the dGPU on Linux).

Windows was a whole lot more troublesome. I could boot into safe mode and disable the Radeon, but that also disabled the iGPU so was left with a "Standard VGA" driver which only has 3 resolutions none of which is appropriate to this display. I uninstalled the switchable graphics driver and Catalyst, but that didn't accomplish much: the iGPU was no longer disabled, but it didn't have a driver either (so Windows falls back on "Standard VGA"). HP theoretically offers a standalone Intel HD 3000 driver for this laptop, but it did not work. Intel has a "generic" HD3000 driver and that did not work either, but at least it had a valid INF so I was able to install it with the "Have Disk" method and got my normal resolution back.

After this, the laptop is almost functional. The only problem is that it appears to be hotter than before -- the fan never turns off now. I'm not sure whether this is because the dGPU is drawing power or because the "generic" iGPU driver is not quite right for the hardware. The heat seems worse in Windows than in Linux.

I suspect the machine's days are numbered, but does anyone have any ideas about how I can reduce the heat? Maybe turn off the broken dGPU altogether or make the iGPU lower its frequency?