Ok this is a physical one.
Temperature is just the total speed of molecule vibrations in an object.
Vibrations are movement. Movement needs energy. All things thrive to be in an energy neutral state, energy always disperses, disbalances are always balanced out.
This means that the natural state of objects is 0°K, the lowest temperature possible, no movement.
That is why you should fill up your fridge and freezer! The only energy you need is for removing heat that comes into the thing and would in turn transfer to cooler objects and warm them up.
But keeping things cool itself doesnt need any energy 🤯
And if you heat it up then less air comes in, and the incoming air will be cooled down faster (energy balanced out between low density air and high density things). So the overall temperature doesnt spike as much and less needs to be transported off.
No, it is not, your premise is false (in our real world. TM.) but your reasoning is good.
Energy does not vanish, you need a process to remove energy of a system.
Think in the planets orbiting the sun or the energy contained in a damm with millions liters of water. The energy is not dissipating itself, it is constant, forever.
So as long as the system is not disturbed, keeping the system in the same state is energy free because you only need energy to alter the system. Even of the energy distributions is not evenly balanced through it.
Disclaimer about the real world