I've got a 12th gen running linux and fan noise is pretty significant when I'm pushing the laptop, but it's usually silent when I'm not pushing it.
Compared to a Macbook Air M1/M2 the laptop is hot and noisy, but really I haven't found it to be any worse than other non-Apple machines that I've used (Lenovo and Acer included).
I expect the Ryzen machines that will be released later this year will be better at keeping the heat down, but that's hard to at this point.
Context: I've got the i5-1135G7 (11th gen) DIY Framework.
99% of my day doing general stuff (work, browsing, banking, etc.), the fan is either off or dead silent (I can't actually hear it at all).
The only time I hear it is when I'm encoding videos, playing a video game, or rendering 3d maps. Stuff you'd expect the fan to be on.
I've got my laptop on a metal laptop stand, which acts like a heat sink, but it also gives the fan ports unrestricted access to air. If you set it down flat on a table, or on a bed, then the fan will likely push harder.
Another i5-1135G7 (11th Gen Intel) here. The fan is only noticeable under load. It keeps the CPU at full power - 2.4GHz sustained - on all cores during Prime 95. Temps stay around 70°C. No throttling. The Frameworks have a high CPU TDP limit which allows for more performance out of these chips which generates more heat and therefore noise. For example, the i5 in mine is pretty much at the top of the Geekbench rankings compared to other laptops with it. Often by a significant margin.
Here's a result from mine with PTM7950.