OK, purely for my own benefit. I had to figure this out.
The coefficient of linear thermal expansion of ceramics is very low. it is about 4 thousands of a millimeter per degree centigrade.
Assuming we can heat the bigger dish to 90 degrees C and cool the smaller one to 10 degrees using hot and cold water then.
Assuming ambient temperature of 20 degrees C then the big one will increase in temperature by 70 degrees and the small one decrease in temperature by 10 degrees.
The big one (200mm diameter) will grow to 200 plus 70 x 4 x 10^-3 = 200.28mm
The small one (190mm diameter) with shrink to 0.19 minus 10 x 4 x 10^-3m. = 189.96mm
The difference due to shrinkage/expansion is .32mm.
However, if the water method is used, it will have to be done upside down since the inner case will just sink down deeper.
I'm googling "upside down filling of a flat pan with water" as we speak.
No results so far.