its not about just being hot, it would have taken many billions of years to get to life.
so no the chance of it being right is slim, there's a good chance we are towards the beginning of advanced life being possible.
then there's as said distances. which are huge. Especially when going between galaxies.
you also have the time constraint, even if advanced life arose before us, doesn't mean they became technologically advanced, didn't kill themselves at various points like atomic age, ai age etc, or that they survived for billions of years to fly between galaxies.
then you have the issue, of what are we looking for, and them looking for us, are radio waves have only just reached a few solar systems and at such a weak strength they aren't likely detectable. Same as with ETs the chance of them using such radio waves like we do is slim, as they don't stand up to the travel of such distances and are to slow for such communications.
so yeah there are literally dozens of issues with the Fermi paradox.