The carbon determination by means of the combustion method is the only real analysis. Thermal analysis (measures temperature) and the optical emission spectrometer (measures light) are comparative analyses.
I found a standard (Part 11) that describes the volumetric method for determination of carbon in the range of 1.50 to 4.50 percent in cast iron and pig iron. The standard also references IS 6226 Recommendations for apparatus for chemical analysis of metals: Part 1 Determination of carbon by direct combustion method (IS 12308-11 (1991): Methods for.....).
I also found a research paper that describes the determination of carbon in certified reference sample Euro CRM Pure Iron 097-1 to 3.98 μg C/g (R = 0.15 at P = 95%) by combustion of the sample portion with subsequent indication of the CO2 by coulometry (Production of reference material........).
I hope this helps! Following references, I hope will help you.
Source:
(1) IS 12308-11 (1991): Methods for Chemical Analysis of Cast Iron and Pig .... https://archive.org/download/gov.in.is.12308.11.1991/is.12308.11.1991.pdf.
(2) Production of reference material | SpringerLink. https://link.springer.com/article/10.1007/BF00487226.
(3) ISO 15350:2000(en), Steel and iron ? Determination of total carbon and .... https://www.iso.org/obp/ui/.
(4) Determination of Sulfur and Carbon in Steel Plants and Foundries - AZoM.com. https://www.azom.com/article.aspx?ArticleID=16229.
(5) Standard Test Methods for Chemical Analysis of Cast Iron—All Types. https://www.astm.org/e0351-18.html.