Dell Latitude 6410 here, my sister's laptop. Was overheating and shutting down, so I purchased a new fan assembly from eBay.
Swapped the fan assembly and had the same issue - system shuts off within a few minutes.
Removed the assembly and cleaned all the old dried up thermal paste on both the CPU (left side) and the GPU (middle area) and replaced it with new Arctic Silver paste. This helped and the laptop would continue running now for about 15 minutes before overheating and shutting down again.
However, when replacing the assembly I noticed how the middle GPU heatsink seemed rather high. Was able to verify it wasn't seating well by reviewing the new thermal paste mark and also by being able to push further down on the middle area after the assembly was already screwed down.
This is an issue of poor engineering. The GPU is overheating because the middle heatsink isn't pressing down hard enough on it to transfer its heat.
The solution I came up with was to use a long nail and anchor it under the plastic area above and to the left of the GPU, go over the GPU heatsink assembly and then bend it down, forcing the heatsink down on the GPU hard and then finally replacing the bottom cover of the laptop to keep the nail in place.
Although you may be able to come up with a more elegant solution, this worked for me and the laptop runs perfectly now with no more overheating issues or CPU stepdowns or noisy fan.
