give him a hardhat.

This condition existed when you bought the house.

Aerosol adhesive applied to the back side of some fairly dense closed-cell foam, and then the foam pressed into place at the head-ache points.

the hardhat idea would be best but I dont think I could convince him to wear it!

We threw some ideas around involving blue gymnasium mat and also the cylinder foam that is used to insulate hot water pipe.
Keep em coming, I am listening!

Another idea that you might consider is some kind of warning device parallel to the beam that sticks out from it a foot or so. He will hit some flexible or movable material first giving him time to duck. A long, thin dowel in held in some large hooks or rings would work. What kind of length are we talking about here?

1/2 in foam Pipe insulation and cut quarter of it out. Then you can glue it in place. You can spray paint it white so it doesn't look so tacky.

I like ionized's idea about hanging something so he can see where he needs to duck. Put a banner or piece of fabric that hangs low so his face needs to go through it. He'll lower his head to go "through" the cloth and hopefully avoid banging his head. Padding it will just provide some cushion, but he'll keep banging into it.

Could you put a piece of furniture in the area under the beam to prevent him from walking there?

I am leaning more toward the "warning strip" approach. A low-mass, or flexible object hung on the side(es) of the beam that would move easily when struck. A dowel hanging in front of the beam would do. Something else might substitute. Someone with a creative mind might make it look like it was purposefully placed there as a decorative element.