Yes. You should make the Production Sourdough with quite cool water, leave it in your kitchen for an hour or two and then put it in the fridge. You can put it in the fridge immediately, but it’s better to give the yeasts a chance to get going a bit before slowing them right down by chilling them to 5°C or so which should be your fridge temperature. The following evening, make your final dough with quite warm water to compensate for the chilling effect of the cold leaven.
You may need to experiment a bit with water temperatures etc, in both the leaven and the final dough. Ideally, your leaven should have risen to near its maximum height in the fridge but should not have fallen back at all. If it has, it may mean that it will be rather acidic. This isn’t a problem as far as flavour is concerned, but it may inhibit the yeasts a bit and lead to a slower final proof (and a late bedtime). If you think of temperature as one of your main control levers, you can learn to perform adjustments that take account of your schedule, the weather and any other variables.