Would This Work?

I was told there would be no math.

My guess is no. The nickel consists of a solid alloy of copper and nickel, not a "copper core" as you suggest. So the idea that there is a significant heterogeneity of thermal conductivity in the nickel eludes me. Furthermore, I believe the effect you would be looking for is thermal expansion, not conductivity. Thermal expansion would be reversible at any rate so intuition tells me any effort to recover a date through thermal processing as you suggest would not be very effective.

Partial acid dissolution (nic a date/vinegar) works pretty well I think, but of course is destructive. If your main goal is to recover the date of a dateless coin without altering the coin and reducing its value, I would urge you to look into acoustic microscopy, a technique that has been shown to do just that fairly successfully by mapping internal strain in the metal induced by the planchet striking process. Then again, this is a specialized technique that is not readily available for low cost analysis.

Even if the date was pushed up would anyone be able read it through all te fire damage?

One thing I hadn't considered earlier: if you were to heat the nickel to red hot in a bonfire, the surface would oxidize quickly, changing the appearance of the coin regardless, but this is besides the point. By heating the nickel to red hot, you would effectively anneal the metal, which results in a restructuring of the internal crystallite distribution. This results in removal of internal strain defects in the metal initially caused by the striking, so perhaps this experiment could lead to the unintended consequence of never being able to recover the date from the coin again.

Since the acid etching relies on crystallite distribution and strain imparted by the striking to create contrast, annealing the coin in a fire would get rid of these features, so you might not be able to do the etching trick on the coin afterwards. I think that would be a cool experiment to try.

Yes. Let's go way out on a limb and say that the main part of the nickel was cupronickel alloy and the part under the date was pure copper (which it isn't). The coefficient of expansion for copper is 0.0000093/degreeF and cupronickel is 0.0000090. So the difference is 0.0000003/degreeF. A nickel is about 1/16 inch thick. So to raise the date 0.001 inches, you'd need to heat it to 53,000 degrees.

My Dad had a Cafe that burnt down and pinball machines that were full of mostly Buffalos and I had these clumps all melted together and warped and I broke a few loose, and I doubt it was 53000 degrees.

The rest went to the bank and they paid us for them