I can only give you my experience.
I have the M1 MAcBook Air model with the 8GPU cores, 8GB RAM, and 512 GB SSD. Have had it since the end on November 2020.
I most often use it in "clamshell" mode with an external display and I really do not see that much difference in operating temperatures vs. open.
In terms of the display, I have an LG 27up600 4K display and I connect it with a certified USB-C to HDMI cable directly to the M1 MacBook Air and it has been working flawlessly. This display was a recent purchase about a month and a half ago. Before that, I was using my old Apple 27" Thunderbolt display which also had no issues.
There are reports of some displays not laying well with M1 Macs gut that seems to be on a user to user basis, i.e. one person reports issues with display model "X" from manufacturer "Y" and yet another one reports it works very well. From what I have been gathering, most of the issues were with older model displays especially when connecting USB-C to USB-C.
I will suggest insure if you are connecting with HDMI that you are using a cable that has been certified by the HDMI consortium (it will state specially on the package or display the HDMI logo).
