A Quartz Thermal Trap Harnessed the Sun–and Is About to Change Smelting Forever

The main tasks in converting iron ore to steel is as follows: reduce the iron (which requires a redox reaction), drive out existing impurities (both other metals present in the ore, such as magnesium or aluminum, and other nonmetals like sulfur or phosphorous), and introduce new ones (predominantly, uh, carbon). Note that these don't necessarily all occur at the same time, in the same furnace (steelmaking is a multistep process). These processes require the necessary chemical reagents to cause the necessary chemical reactions to occur.

There are multiple roles for heat. Most notably, most of the necessary chemical reactions require high heat to occur at a time. Furthermore, outright melting gives the advantage that impurities tend to sort themselves by density, and your impurities are typically less dense than your main metal (i.e., the slag will float on top of the molten iron). There's also the advantage that high heat can make volatile impurities (e.g., sulfur dioxide) boil out.

Historically, the reducing agent was largely charcoal, where you burn the wood in oxygen-poor environment to produce high purity carbon-rich material. The industrial revolution replaced charcoal with coke, where you burn coal in oxygen-poor environment to produce high purity carbon-rich material. In both cases, the furnace converts the fuel largely into carbon monoxide, which is the main actual reducing agent in contact with the iron (whereupon it forms carbon dioxide). The decarbonization assumption has been to replace carbon with hydrogen gas, but as far as I'm aware, hydrogen-based reduction furnaces have only existed in pilot plant form.