Do you have a lot of extensions in Firefox compared to Safari? That's often why Firefox is »heavier« on memory and CPU. This combined with Apples fan-curves, that basically wait until the laptop is really hot before it kicks in the fans at full speed can create the annoying result you're describing.
If Youtube is the only issue, it could also be related to Youtube and not Firefox. Some websites (Google's search fx) serve up different versions of websites for different browsers. Youtube is a Google company.
I'd recommend checking if there are some extensions you don't need anymore, or if you have several extensions doing the same thing that could conflict with each other. Fx having several ad- and tracking-blockers can often work against each other. Ublock origin has the best coverage and should be the only one needed in most cases.
A personal note on Macbook fan-curves: To combat Apples fan-curve issue in general, I'd recommend installing Macs Fan Control: It'll let the fans kick in earlier and at a lower speed so they won't be as noticeable. And it'll cool your mac more effectively (rather than waiting until it has gotten very hot).
