No Reverse when cold, but works fine when warm.

We have a 2008 with 214,000 miles that when the transmission is cold, it
does not have reverse.  It goes through the forward gears just fine and no
signs of slippage.  As the transmission warms up, reverse will begin to grab
but let go.  Finally at some point when the transmission fluid fully warms,
reverse works just fine.
At no point is there any feeling of slipping.  The reverse either works or it
doesnt, even at that inbetween period where it will start to back up then it
just lets go completely.  
I'm thinking with the lack of slippage and the fact that when its warm it works
fine means the likelihood of it being clutches or drum seals being the issue is
low, and it is more of a sticking valve issue?
Contemplating between a fluid change and a complete fluid flush?