We have two identical massive metal spheres at the same temperature at rest in free space. Both have an identical charge and the Coulomb force [plus the black-body radiation pressure if the temperature is non-zero] exactly counteracts the gravitational force between them, resulting in no net forces on either object. They are electrostatically levitating at rest in space. It is my understanding that the charge distribution in each sphere exists only at the surface, and should be concentrated on the side facing away from the other sphere.
Now heat one of the spheres uniformly with an external energy source. What happens in the instant following?
Could it be: The increased mass-energy of the hot sphere increases the gravitational force, and the cold sphere starts to fall inward.
Or else: The increased temperature modifies the charge distribution on the hot sphere by giving it more variance and bringing it closer on average to the cold sphere, increasing the Coulomb force. The cold sphere starts to fall away. [Carl's answer says there is no effect on the charge distribution like I describe, but DarrenW points out that there will be an increased black-body radiation pressure between the spheres, similarly causing an outward force.]
Which direction is correct, and what is the best explanation? Does it depend on the amount of temperature change or the initial conditions?