I have had multiple MacBook/MacBook Pro's, never had an issue with overheating while using external monitors. At one point I had 3 hooked up to my MacBook Pro.

The key thing is to not use it in clamshell mode.

Also DisplayLink wouldn't really help much with running cooler, since its drawing a virtual frame buffer using your existing graphics card anyway, although I don't know if macOS would recognize it and switch to the discrete graphics when in use vs continuing to use the iGPU.

I have two big monitors, I do not have space on my desk to keep laptop lid open (and that would be waste, because I would never even look at built-in screen anyway).

As for running cooler it really did change for me after buying DisplayLink docking station - before I would hear the fan noise constantly, now the laptop just stays quiet.