It started out quite shapeless:

The instructions say to block it on a dinner plate of the correct size:

After it was blocked it turned out really nice.

(DH says it looks frosted in the middle; it is just the way the variegated thread turned out.) DD2 has been encouraging me to line it so it would be warmer. At first all I could think of was to knit another tam, adding it inside out to this one, but that would be a lot of work. Then I thought of felt, but that wouldn't be very soft. Then today, at the grocery store I saw knit hats lined with fleece, and I thought "Eureka!"
I also need to add some elastic to the brim, just to tighten up a little. It turned out so pretty, though, that I think the extra effort in finishing it will really be worth it. It is knit with the same thread I used for my windowpane scarf:

I have enough yarn to make matching mittens too, in the yellow/red range.