If you are willing to use some engineering judgement and avoid the cost of subscribing to a database you would only use on rare occasion, I would offer the following;
typical value of specific heat for carbon steel (less than 0.3% ) @ 650 deg F is 0.143 BTU/lb deg F.
I have seen limited data on Poisson's ratio at elevated temperature for carbon steel. There does appear to be minor change (increase) with respect to test temperature, so I would use a value of 0.3 @ 650 deg F. Actual value at room temperaure varies from 0.28-.29 for carbon steel.
The shear modulus (G) can probably be calculated by using the relationship between Poisson's raio, Young's Modulus (E) and the shear modulus (G). For carbon steel at 650 deg F, E is approximately 26 X 106 psi. Thus, the shear modulus at 650 deg F should be about 10 X 106 psi.