ASTM A 551 Standard Specification is for Steel Tires used in railway and rapid transit. Class C material is for untreated tires, used in switching locomotives.
The following chemical composition range applies to Class C material;
Carbon 0.70-0.85%
Manganese 0.6 - 0.90%
Phosphorus 0.050% max
Sulfur 0.050% max
Silicon 0.15-0.35%
As far as an equivalent AISI steel grade, the closest matches are either AISI Type 1078 or Type 1080 carbon steel. For heat treatment, A 551 only specifies a “slow cool after forming to accomplish proper transformation without damage”. For the AISI material equivalent, I would have it supplied in an annealed condition.