Maby Sapphire X1650PRO/XT (active cooling - height the same as an blind ) or 7600GS passive (ASUS, Leadtek and MSI has one with heatsink only).
If you have some place above card then MSI has Radeon X1650 XT with HeatPipe
which should be good.
And Gigabyte has 7600GT SilentPipe II rev.3.0
, but I don't know if it fits
It looks thin.
I forgot about HDMI...
It is hard task. That Radeon X1600PRO from Sapphire has and it's low-profile. I am not sure, but MSi has NX7600GT Diamond Plus
. And it look thin also