Why? It will just end up with a bigger heat sink to cool both the SSR heat and the additional heat the peltier will add to the system. Besides there is no need for the SSR to be cold, just not overly hot.
I second this..I have a few peltier devices and they use a lot of energy and create a lot of heat on the opposite side...I dont think it will be as nearly efficient as an aluminum heat sink which works fine and cant fail like the peltier.
Would never be able to sink the heat. Even if you could get one big enough for the application, it would need a heat sink 4x as large as the one for the SSR alone. Dont bother pursuing this, there is nothing to gain.