Make Ubuntu silent, even in expense of decreasing speed

I have an Intel i3 mini desktop pc, which is used for home server, mainly for Plex. When a user requires certain kind of video transcoding, the machine spins up its fan very loud, instead of it's otherwise really quiet mode. I am looking for some easy to set up instructions, which allow me to use the machine silently whatever happens on it. I don't care if it can't serve my users well enough (then they have to choose direct streaming for example), my highest priority is to reduce maximum noise, so maximalize fan speed. What are the common solutions for capping CPU processing power, to not let it overheat to the level which needs intense fan cooling? The Linux is an Ubuntu 22.04. The machine is a Gigabyte GA-H81N-D2H motherboard + Intel Core i3-4130 3.4GHz. The case has only the CPU fan.