Every thermal storage has losses and BILS will therefore potentially heat up their hosting lake. Of course this is depending on several paramaters such as the operating temperature of the storage, the size of the BILS and the lake and the insulation, etc. 

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Considering the case of the lake of Zurich:

Assume a cylindrical BILS with 40 m diameter and 40m height (approx 50 Mio Liter capacity), normal insulation, storage temperature over the whole year at 99°C and lake temperature constant at 4°C. For such a BILS, the annual energy losses will be in the range of <2 GWh/y.

On the other side, the energy scenarios of the city of Zurich estimate that in 2050 about 2-4% of the total heat demand will be provided by the lake. This is about 30-60 GWh/y energy that is extracetd from the lake. (The total potential of the lake is estimated with 5000 GWh/y to more than 10'000 GWh/y. )

Comparing the 2 GWh/y losses of the BILS (-> heating up the lake) with the 30-60 GWh/y extracted anyway (-> cooling down the lake) shows that even very large BILS will not affect the lake temperature in a negative way. In contrast, it will compensate about 3-6% of the energy that will be extrated anyway. 

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Even a similar BILS with 500 Mio liter volume at 99°C will provide only about 9 GWh/y loss, meaning that the problem of heating up the lake is virtually not relevant,