Do you have a full-auto double??

I hear you. I haven't done a whole lot of shooting with mine but I agree that the barrels get quite warm in short order. I prefer to place my front hand close to the muzzle end of the foregrip in a manner that allows my front finger to "roll" over the edge.

I think the key when using a rest is to allow the rifle to recoil as naturally as possible. Several folks mention employing a standing rest though I have have well with a sitting rest as long as I keep my body in a fairly upright position.