Does anyone know why blackbirds 'sunbathe' with their beaks open?

When birds get too hot they open their mouths to cool off. It is similar to a mammal panting to cool off.

I have seen baby blackbirds sit with their wings outstretched and beaks open when they are waiting for the parent bird to come back to feed them. Maybe that's what you are seeing, but I'm not sure.

A bird will drop its wings down and fan its tail feathers out whilst bathing in the sun to help increase its body temperature.

It could also have been 'anting' where the bird actively allows ants to crawl over its body (either by placing ants onto itself or by actually lying on top of an ants nest), the ants will 'defend' their nest from their 'attacker' and the formic acid produced by them will help reduce the number of external parasites (i.e mites) on the bird.

I don't know about blackbirds, but my bearded dragon opens his mouth when he is too hot. Somehow it helps him regulate hi body heat.

To lose body heat when hot.

They wear little headphones in their birdie ears. Then they sing softly along with the American Idle stars (they download the music).

cause the top of their mouths dont' sunburn