It is due to unreduced FeO. High FeO in slag and low HM temperature come together because they have the same reason - too much Fe must be reduced by strongly endothermic reaction FeO+C=Fe+CO becuase less heat consuming reaction FeO+CO=Fe+CO2 is by some reason suppressed (by worsening BF gas distribution e.g.). But start worrying about FeO in slag only when you see its more than doubling from normal level (>1.0% instead of normal 0.5% e.g.). Also FeO in slag is very slow and very not obvious sign of BF cooling - much better is slag T, HM T and HM Si and HM S. So I propose ignoring FeO in slag.
When BF gets cold, FeO in slag increases and Si in HM decreases. In this moment SiO2 in slag grows (Si in hot metal reduces less) and there is relationship between SiO2 in slag and FeO in slag. Only in such way I see this relationship.
An increase in FeO content in blast furnace slag typically occurs due to increased iron oxide in the iron ore, which can be caused by various factors using more fine ores, higher levels of iron oxide impurities, and changes in the smelting process that lead to more iron oxide being dissolved into the slag phase, amount of oxygen available in the furnace. Ageing of BFS also affect the FeO content in blast furnace slag.