If the characteristics of Tempurpedic foam are in any way similar to other types of upholstery cushion foam, I would be VERY careful to not let any moisture migrate too deep within it.
I made the mistake once of trying to hack out several inner foam upholstery cushions by submerging them in a tub try to flush out Chihuahua pittle.
They absorbed so much water that they weighed 25 pounds heavier when I tried to take them out, and it took me a week to fully dry them out.
The cell structure of such foam must be so complex and integrated that any liquid will continue to migrate deeper and deeper within.
Fooking things were fully saturated and they would barely even drip.
Had to SpaceBags them for a day each to squeeze and extract all the water out of them.
Big mistake.