Cast Iron also requires much higher temperatures to produce than the ordinary wrought iron/low grade steel that was typical of Medieval Europe (smelting iron = temperatures of 900 - 1200 C, cast iron up to 1530 C). China was producing cast iron from about 500 BCE, because they had built kilns for firing porcelain that reached nearly the same high temperatures as for cast iron!
BUT if we start building a game of Medieval Technology, it gets ridiculously complicated and not much fun at all. Simpler to just allow Coal or Charcoal to be used instead of Firewood, say, only after you have Tier 3 metalworking like Tools - ‘Tools’ in this case could be the ironwork spits, spoons, skillets and pots to cook with the higher temperatures from coal, which would both impose an extra cost on heating each house (having to provide ‘tools’ for each House) and provide a high-end alternative to Firewood.