Hi VP93Navy
It's not quite that simple. This is from NIST "The Gauge Block Handbook" by Ted Dorian and John Beers (page 28).
"The uncertainty in the expansion coefficient of the gauge or workpiece is more difficult to estimate.
Most steel gauge blocks under 100 mm are within a five tenths of 11.5 x 10 /oC, although there is
some variation from manufacturer to manufacturer, and even from batch to batch from the same
manufacturer. For long blocks, over 100 mm, the situation is more complicated. Steel gauge blocks
have the gauging surfaces hardened during manufacturing so that the surfaces can be properly
lapped. This hardening process affects only the 30 to 60 mm of the block near the surfaces. For
blocks under 100 mm this is the entire block, and there is no problem. For longer blocks, there is a
variable amount of the block in the center which is partially hardened or unhardened. Hardened
steel has a higher thermal expansion coefficient than unhardened steel, which means that the longer
the block the greater is the unhardened portion and the lower is the coefficient."
I interpret this as meaning, you need to calculate your own personal thermal expansion coefficients for your particular gauge block set. I expect that there is not much difference between different sets in reality. But if you are concerned, perhaps 'not much' is rather a lot.
You might find the handbook useful. It's available as a pdf from NIST. Just search on the title and names and I expect you will be able to find it.
NC