The energy that goes into doing calculations must end up *somewhere*. Conservation of energy doesn’t stop when you use the energy to do calculations, or do anything else for that matter. Either the energy that you use to do useful things is stored somewhere where it can do more useful things, e.g. in a battery or a compressed spring or a fidget spinner, or it gets wasted as heat and can’t be used usefully anymore.
It just so happens that we don’t have the means to usefully store the energy that goes into performing calculations anywhere. Moreover, the fact standard CPUs are *irreversible* computational devices means that there is a fundamental minimum amount of energy lost in performing those calculations. However, this is a small fraction of the overall energy that gets wasted as heat in modern processors.
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