The earth’s core is about 5500C and is mostly composed of iron and nickel, probably. Presumably, it would shrink tremendously going from 5500C to 0C so in theory you could calculate the rate of shrinkage using iron’s rate of thermal expansion. However the core is also under immense pressure which makes iron much denser (smaller) than on the surface of the earth. The immense temperature and pressure is a result of the action of gravity pulling the core onto itself.

The short answer I think is the earth cannot exist as we know it at anything below its core temp of 5500. Suppose we waved a magical wand that set it’s temperature to 0, it would implode on itself (along with the rest of the planet) and heat right back up to its current core temp of 5500 before you could measure the effects of thermal expansion.

67% of the Earth’s mass is comprised of silicates in the mantle. Solid silicates have very low thermal coefficients of expansion, meaning they change volume very little in comparison to other compounds. So if the mantle was cooled and solidified to 0, then heated to 50, it’d have very little effect. It’d grow something like 0.02% in volume.

Being that the mantle is generally liquid, you’ll see a much larger effect from the initial cooling. But how much? I don’t know. Liquid rock isn’t present in mere mortal online calculators and my ability to dive into the material properties and manually calculate it is long gone from my head.

But “much” larger may not be significant to the human experience, given that 0.02% would be imperceptible as a baseline. If you had a 1km long solid silicon ruler, heating it from 0 to 50C would make it just (edit) 0.2m longer. A circumferential ruler reaching around the Earth along the equator would go from ~40,000km to 40,008km.

Edit: corrected 20m to 0.2m. Flubbed the percentage in the calculator as 0.02 (2%) instead of 0.0002 (0.02%). So really, really imperceptible to a human walking 1km