Does a hotter processor run faster?

Does a hotter processor run faster?

I heard from a physicist that when silicon gets hotter it can conduct more
electricity through it. He said:
"Silicon is going to have a pretty good structure, it's going to have
higher melting point, but as we increase the temperature we start to
vibrate those atoms and it can actually be a conductor. It's something we
call a semiconductor and so we can vary the amount of electricity
conducting through it. And one way we can do this is to dope it, we can
add different elements to it, different other atoms, we can n-type or
p-type dope it, and we can add either electrons or lack of electrons, and
so it allows us to create transistors."
This is of course not written but spoken text in this video.
But it made me think, when a silicon chip get hotter does that mean it
gets faster and produces better performance, and does this count for
processors as well?
I'm aware that the question is a bit odd, especially because I do not
fully understand the architecture of a processor, so I'm curious about
what the answer is.