This is an older (maybe 5 or 6 years) 40" LCD TV and I'm happy to report that the new AppleTV works great with it controlling the volume as well as turning the TV on and off. The volume control worked out of the box without my setting or changing anything (and frankly, I have no idea how, if it's using IR you'd think that you'd need to tell the Apple TV what codes to use, but maybe it was able to identify the TV through the HDMI connection). Turning the TV off with the AppleTV remote worked out of of the box too... put the AppleTV to sleep and the TV powered off too.
Unfortunately, turning the TV on with the AppleTV did not work out of the box... the AppleTV would go on, but not the TV. After a little playing around I discovered that by going into the TV settings, selecting Option, Then "AQUOS Link Setup", then changing "Auto Power On" to Yes will allow the AppleTV to turn the TV on when it comes on.
So at this point I can turn the TV on and off and control the volume all with the AppleTV remote.
Unfortunately, turning the TV on with the AppleTV did not work out of the box... the AppleTV would go on, but not the TV. After a little playing around I discovered that by going into the TV settings, selecting Option, Then "AQUOS Link Setup", then changing "Auto Power On" to Yes will allow the AppleTV to turn the TV on when it comes on.
So at this point I can turn the TV on and off and control the volume all with the AppleTV remote.