We can also time shift many of the things we do. Does your fridge need to run between 3-5pm in the heat of summer? or can it make sure its a little cooler to avoid running then? (trivial example, probably not a good one)
I'm sure there are better examples, but your fridge idea doesn't work. Fridges already operate on the edge of freezing, so if you make it a little cooler you will ruin all your food. Also 3-5pm is peak hangry time.
This is why a major part of the solution is electric vehicles. Why put batteries in a warehouse and then run vehicles on petroleum when you can put batteries in a vehicle, install twice as many renewables because you now have more demand for electricity, and then charge the vehicles when generation is a large percentage of rated capacity and still have enough to run the rest of the grid when it's a smaller percentage?
It will be a mix. There is certainly still a lot which can be done on the demand side, e.g. when to cool a cool storage house during the day, or when to run certain production lines.