Sometimes, even just a flat piece of aluminum or copper that has more surface area will do the trick. Not sure about cooling an SSD, but I don't imagine it would put off much heat, and this would likely be sufficient. I am trying to think of OEM products that have used a similar cooling set-up, but I can't think of anything off the top of my head...it's fairly common to see though in various electronics. So just try a chunk of flat aluminium in whatever size and thickness you think you can fit in the space there. You can even cut down some little ram-sinks or something and sand them to mostly flat. You can attach the flat heat sink with some double sided thermal tape, or get some thermal adhesive, both will work. Make the heat-sink have as much surface area as you can fit in the space you have available. but be sure to leave an air gap so air can still flow around it. If it is fitting right up against the outer case of the laptop, you could use some single sided thermal tape between the heat sink and the case, but if the case is plastic, that isn't going to do much.
Like this, if the drawing makes sense to you -
