On the granite block idea, many ovens have a time bake feature where you set the time for the oven to come on, no early wake up needed.
On your trial run, you need to address the effect of cold on the entire lunch bag, not just the base. Maybe you could find a willing walk in freezer owner.
How big is this lunch bag? lol, i had fun running tests before just in a regular freezer/refrigerator. Then again my fridge/freezer isn't full of too much food.
Agree with the preheat, that's vital to keep hot things hot, not get cold things hot.