What PS3 model can play PS1 games and PS2 and actually works / doesn't overheat?

The ultimate PS3 which model can play ps1, ps2 and doesn't overheat?

Bought the PS3 around launch, could play the ps1/2 games without any problem... good thing it could as it didn’t have anything worth playing for several yearS..

How hard is it to google?

This is not a System Wars topic.

And a quick Google would show you there's only one PS3 model that offered full* bc

*with some exceptions like guitar hero