Temperature differences are what drive heat engines, i.e. you need a hot and a cold(er) reservoir. A nice demonstration of this is a handheld Stirling engine, which you can power by placing ice at the bottom (since it’s colder than the surrounding environment).

Okay, but technically you're storing the energy in the environment, not in the cold reservoir. Maybe a distinction not worth making.

0 - you must play the game

1 - you can never win

2 - you can only break even on a very cold day << f.n.

3 - it never ever gets that cold

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f.n. >> the maximum efficiency of the work that can be extracted from a heat cycle is dependent on the relative difference between the hot end and the cold end and absolute zero. The closer you can get the cold end to zero relative to the hot, the higher the efficiency. The energy of a heat engine comes from the potential. If everything is equally hot there is no potential energy just as much as if everything is equally cold. If there is a gradient, you can do work.