This question looks like an XY problem, so I'm not going to address monitors at all but instead how to fix your overheating problem in the first place.
Apple laptops do not like to use their fans. Usually, the only reason they overheat is because the fans don't turn on soon enough. If your fans are running at full speed with the Apple fan curve (which hates to turn on the fans), this is a very bad sign.
The solution to your overheating problem is to turn the fans on sooner. There will be more noise, but your laptop will not overheat. You can do this by using an app like Macs Fan Control to run the fans at full speed before overheating happens. I've run extremely heavy loads on my laptop, including running multiple games at once, training a neural network, and rendering complex scenes and it has never throttled, not once, except in cases where I forgot to turn up the fans.
If you want to avoid all fan noise however, then I've got bad news. Apple already tries to avoid fan noise, and by doing that they starve the laptop of the cooling it needs and drive it to thermal throttling.
If you want to prolong the life of your laptop, I would recommend getting used to the noise (it's really not that bad). Overheating can damage critical components including the CPU and GPU themselves.
And especially if you have a newer laptop, any broken parts can mean a total replacement, and your data gone. Better safe than sorry.