Does liquid iron have a constant specific heat capacity? Everywhere I've looked (save one sourceless online reference to $C_p$ = 611 J.kg–1.K–1 here), I find no value listed for liquid iron. Is this because the heat capacity is temperature-dependent? Or is this related to a measurement problem? Or does an accepted constant value exist, but I'm just a poor researcher?
Okay, let's answer bit by bit:
Heat capacities are usually dependent on temperature except for ideal gases. You will generally find the values tabulated at specific temperature and pressure values. For instances for which one is interested in heat capacity as a function of temperature, this is usually approximated through a regression equation. The NIST JANAF Themochemical Tables use the Shomate equation with 5 coefficients, of the form:
Cp° = A + B t + C t2 + D t3 + E / t2
where t is T (in K) / 1000, and A, B, C, D and E are regression coefficients.
If one looks at the Condensed phase thermochemistry data page for iron, one can find the relevant coefficients (A, B, C, D and E in the above equation) and thus calculate heat capacity of liquid iron in the 1809 - 3133 K range. Since all coefficients except A are close to zero, for liquid iron heat capacity is nearly constant in this range.