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Heat is really useful if the energy form you want is heat. If you want electricity or motion it's not the best.
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"What, sir, would you make a ship sail against the wind and currents by lighting a bonfire under her deck? I pray you, excuse me, I have not the time to listen to such nonsense." (Napoleon Bonapart ~1800)
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It's inefficient, but still better than completely losing out on it. Better yet would be direct reuse or remote heating.
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That depends on what you need energy for. Converting heat energy stored during the day to heat my house at night is easy. Converting heat energy stored into light is much harder (as the other reply stated, it needs high heat and thus is a fire hazard)
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Heat can't be converted losslessly to useful energy, but converting to heat to other forms of energy is extremely common. What do you think a steam turbine, boiler, internal combustion engine, etc. do?
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But all the examples you give have a heat source of high temperature and dense energy, and a lot of energy is lost in it's transformation, as illustrated by the combustion engine. How can heat be a good energy storage if so much is lost when you want to use it?
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If it's free to collect (solar) then efficiency matters a lot less.
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It isn't just the cost to collect, it is also the cost to store. Heat is easy and safe to store at just above room temperature in rocks - but you need a lot of rocks. Just to heat my house for a few days would need tons of rock at temperatures I'd allow in my house (I have kids and so I worry they will open the rock container and get burnt). Rocks are not free. You can also use water for storage, but again you have the issue needing a tank (and water is a drowning hazard, plus the worry about leaks...)
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Square cube law will optimise heat storage. These Finnish sand based heat batteries are a prime small-scale example.
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"Low grade heat", less than the boiling point of water (often), can be stored in a sand system and recovered efficiently and distributed later.

But low grade heat cannot efficiently drive a heat engine to produce other, more useful and transferable versions of energy, like electricity. For that you need "high grade" heat.

The reason is, heat engines do not operate on heat. They operate on heat flow. You must have a high temperature side and a low temperature side, and you extract energy by taking heat out of the high side and injecting it to the low side, through various processes. By thermodynamics, this process has hard efficiency limits of around 35%, with that efficiency heavily affected by the delta between the hot and cold side.

The "low" heat side is often a great source of low grade heat, for industrial or communal purposes, but cannot be used to run an efficient heat engine. It's already "used up" essentially.

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The "grade" you refer to is simply temperature. To efficiently extract energy from a heat flow you want a really hot hot side and a really cold cold side. On earth we can't get a cold side much colder than outside air temperature (not without wasting more energy than you gain) but luckily that is cold enough when the hot side is thousands of degrees. But you can't get much energy from roomtemp and roomtemp+10. A warm cup of coffee will run a Stirling engine for a party trick, but it's not going to charge your phone, much less your car.
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Nuclear reactors do exactly that
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A lot of energy generation is just "produce heat, boil water, steam moves a turbine

So in that regard heat is very useful in producing energy. But converting directly from heat to energy? Not so much as far as I know.

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Yes. This is sometimes called "Carnot tax".

The efficiency of any heat engine is bounded by the Carnot cycle. In simplified form, it depends on the temperature differential between the cold and the hot parts. So if your hot part is at 300C (572 Kelvin), and the cold part is at 30C (300 Kelvin) then the absolutely best possible efficiency is around (572-300)/572*100% = 47%.

You see that it quickly becomes inefficient as the differential goes down. E.g. if you use 90C to store the heat, then the maximum efficiency is just 17%.

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Use it directly, see my silbling comment.
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so all such 'energy' storage are to be used as heat and no other form of energy? The name energy storage is somewhat confusing then, even if not incorrect? Heat storage would be more accurate iiuc.
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