I also think the battery will be OK. It's the rest of the computer that concerns me a bit.
M-series Macbook Airs do not have cooling fans. They rely on convection cooling like the original G3 iMacs. Even Apple laptops with fans let some heat escape through the keyboard area. I'm writing this on my M4 Pro Macbook Pro that has two fans, and I can still feel a little warmness when I hover my hand over the keyboard. The aluminum case can also help dissipate heat
Using an external monitor can increase the workload on any laptop. Your computer can cleverly monitor its own thermal health with sensors placed on key components and areas. Apple handles high temps by first clocking back the processor to a slower speed. Depending on what app you use, you may notice a slowdown. If the thermal system cannot manage the heat by clocking, it can shut down the computer to save its brain.
Heat produced by a computer is, as with the human body, directly proportional to the workload. Rather than my taking a "shotgun" approach to my questions and comments about workload, how about you tell us what tasks and apps are in play during those four hours? If four hours of work requires a a browser, please tell us which one you use. Not all browser are equally created when it comes to workload.
You are probably totally fine, but the real determining factor is the nature of your workload.