TotallyUsefulFactory.cs

public class ThingFactory
{
    public string ThingName { get; }
    public string ThingValue { get; }

    public ThingFactory(string thingName, int thingValue)
    {
        if (thingName == null)
            throw new ArgumentNullException(nameof(thingName));
            
        ThingName = thingName;
        ThingValue = thingValue;
    }
    
    public Thing MakeThing(string elusiveThirdParameter)
    {
        if (elusiveThirdParameter == null)
            throw new ArgumentNullException(nameof(elusiveThirdParameter));
            
        return new Thing(ThingName, ThingValue, elusiveThirdParameter);
    }
}