I was given a Compaq CQ50 laptop which was overheating over the course of 30-60 minutes and reaching a temperature where overheating protection kicked in and the laptop abruptly shut down.
A quick search for a solution turned up many results. Many revolve around the GPU overheating specifically. I combined a few approaches. I could not find a technical manual for the internals of the CQ50 but there are a few disassembly videos on YouTube. I liked a video posted by ThibaultServices best. Disassembly to get at the relevant parts was more involved than I anticipated: CPU heatsink/fan, GPU heatsink, and rear case plastic. Here is a picture of everything once it has been disassembled.
I made three changes which I feel were effective.
Cleaning lint out of the the CPU heatsink and fan is an obvious improvement for any laptop. Most videos I watched and forum threads I read mentioned that there was quite a bit of lint trapped in the area underneath the heatsink's fan. My situation was no different.
As mentioned in this lengthy blog post the fans are not placed well with only one intake on the bottom of the case and an exhaust nearby at the bottom/rear of the laptop. Similar to a YouTube video posted by Gt-R Vspec, I added ventilation directly over the CPU and GPU.
I eyeballed the heatsink's location within the back plastic to estimate and mark with pencil the location of the CPU and GPU underneath. The holes in the aforementioned video were drilled but in my case I used an old soldering iron to melt the holes through the rear plastic case. I also smoothed the holes with sandpaper.
Following the advice in this forum thread, I cut two strips of double-sided foam and stuck them to the existing pads of foam on the heatsink pipe so that the addition of foam presses against the back panel and pushes the heatsink down onto the GPU for better contact.
While I had everything open I also cleaned the existing thermal paste off of the CPU and removed a square of putty that was between the GPU and the heatsink. Just before reassembling everything I put fresh dabs of thermal paste on the CPU and GPU.
After closing everything back up I've been very satisfied with the results. With moderate use the CPU is able to better regulate its temperature and maintain 50°C. The GPU is much cooler and the general motherboard temperature within the laptop remains completely constant.