eli5: if you need to put energy to rise the temperature of the substance, why cant you generate energy by cooling something down?
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It’s important to understand what is meant by “generate” when we talk about energy. At the most fundamental level you can’t generate energy- it can’t be created, only moved from one place to another and usually by changing its form (kinetic to electrical, or thermal to kinetic to electrical, for example).
For example, you can’t make energy from a hydroelectric dam unless there’s water above it to fall through the turbines. In order for the water to be up there, it had to be moved via evaporation from lower areas, carried by the wind, then dropped as rain on higher elevations. The energy to do that came from the sun- at no time did the dam actually “generate” energy, except in the local sense- by changing the kinetic energy of the water into a different form. We say “generate” because it’s generating energy in a form we can use directly- electricity- to power stuff, but under the hood it’s changing energy from one form to another.
To be able use energy to do any useful work, it must move from one place to another- the dam must have water flowing through it, for example. Without that motion, there’s no energy.
If you want to create usable energy from moving heat from one place to another, you have to be able to have a difference in temperature and a way to move the energy from one temperature to another. Geothermal energy is one example- using heat from the planet to boil water into superheated steam, it’s carrying energy from the hotter point through turbines or other energy-conversion systems, which generate electricity, and consequently cause the steam to cool down.
But you always have to move energy and that means you’re moving it from where there’s more energy (the reservoir behind the dam, the hot area in the earth’s crust), to where there’s less- the turbines that generate electricity. Along the way, the means of carrying the energy- usually steam- loses that energy and becomes cooler. Some of the energy is converted into electrical or mechanical power, some is lost as waste heat.
So, when you think about it, generating energy *is* “cooling something down” (when you consider “cooling” to be “reducing its available energy”). Using geothermal power takes an infinitesimal fraction of the heat away from the source, and using hydroelectric power takes energy from the system by letting the water flow.
But the energy has to flow from the higher energy state to the lower one- until both states are equal, which is what all energy in the universe seeks in the long term.
Coda: Car brakes do the same thing- by taking the kinetic energy of the vehicle and turning it into heat via friction, it reduces the velocity of the vehicle. Brakes on your car are literally just heat transfer systems.
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