Which ball has the greater acceleration at the instant of release

I can't see either of them, so I must assume that they're both
far away from me, at different places in the solar system. 

So I can say with some assurance that whichever ball is on the
more massive planet will have greater acceleration when it's dropped. 
Its acceleration will be constant, from the instant of release until the
instant it hits the "ground" or whatever they call it on that planet.

The sample with the lowest specific heat capacity will have the greatest temperature increase. in this case, it would be platinum.