Based on the temperatures and CPU usage you shared in the chat, I believe that what you are experiencing is normal as reviving video over the internet and deciding it is very taxing on it. However a CPU cooler isn't exactly a necessity as the Pi will simply slow itself down to prevent it from over heating. But if you want to watch YouTube in a higher quality or have background tasks running while watching YouTube then I would recommend a heat sync and maybe a fan to prevent thermal throttling.
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