The board already started to rot from below, so I need to replace it. How can I seal this small gap without having a permanent seal? The problem is that the boad is attached to the wall and I still want to be able to move the sink table away from the wall to get access to the tubes and things that fell behind the sink.
I have to say, this is a very uncommon situation. I have never seen a radiator behind a sink or heard of a movable sink table. I guess you have your reasons, but would it be easier to put doors on the front of the "sink table" so you can access the plumbing etc without moving it?
With that said, the first thing I'd recommend would be replacing the wood board with a rot proof composite or PVC board. I'd add a 2 or 3 inch vertical splash board around the opening by the heater so water and objects won't fall down behind the sink. With the sink in place, maybe you could use a thin bead of acrylic door/window caulk to seal it to the wall and board. If you find that you must move the sink on occasion, the acrylic caulk is easy to remove and simple to reapply. Another alternative you might try is a strip of self adhesive rubber pillow style weather stripping to seal the gap between the sink and wall.
If cosmetics isn't an issue you could use foam copper pipe isulation. It comes preslit and somewhat heat resistant. Open it up along the slit and slide it over the board. It appears to be a radiator behind the sink so any thing you use must be flexible as the radiator will expand and contract as it heatsup.
Remove the wooden board and replace it with cement board, then tile the area.
