Dell Precision M4500 overheating when attached to 32" monitor running at native 2560x1440 resolution

I'm posting this more as an observation of things I discovered than as a question, but would welcome feedback from others experiencing a similar problem.

At the Black Friday sales I bought a very nice 32" Asus VA32A 2560x1440 WQHD monitor to use with my Dell Precision M4500 i7 laptop. I was replacing a smaller very old Dell monitor that had a considerably lower maximum resolution.

Almost immediately I started experiencing events daily where the screen would turn a nice shade of mauve in pixelated pattern and freeze, requiring a hard reboot. This had happened on very rare occasions before, but not often enough to investigate. Now it was a constant problem and everything I read online told me it was an overheating issue and not to ignore it as it could destroy the computer.

First recommendation was to clean the dust out of the fan area. Being an old computer there was a lot. I took out the fan/heat sinks cleaned the input and output screens as well as the fan itself meticulously and put it all back together. No benefit; still overheating.

I figured maybe I had accidentally removed come of the thermal grease so took it apart again and replaced the grease where it was previously. Same result - still overheating.

I then bought a cooling fan for under the laptop and made sure that the laptop's own monitor was turned off when the case was closed (I use an external wireless keyboard for this setup. It seemed to make a difference and SpeedFan and RealTemp appeared to reflect an improvement but the darn thing crashed again, though not so frequently.

Then I read online that the problem might not be with the size of the monitor but rather the resolution. So reluctantly I stepped down from its optimal resolution (the reason I bought it in the first place) and ran it at 1920x1080. It has not crashed since (touch wood).

Even if it does crash again, I now know that the problem is indeed a result of overheating and that it is attributable to an external monitor placing too much demand on the built-in Nvidia QuadroFX 1800M GPU. Since I cannot replace that, I either have to get used to using my monitor at less than optimal settings or sell the monitor and go back to a lower resolution one. Neither solution is particularly appealing.

Any comments/thoughts?