My preferred fantasies are superconducting electronics or photon based circuitry.Also adding in fantastical ideas here's a Popular Mechanics article about the possibility of 'Next-gen' computers that would work at 450C. With those you could combine power storage with data centers.
High-Temperature Semiconductor Computers - Next-Gen Semiconductors - Popular Mechanics
But the requirement of high temps doesn't require much energy. This is because
once a closed system is up to operating temperature, insulation makes energy
demands low. So I argue that it's better to recover usable energy from waste heat.
How best to store it? The market will sort that out. Right now, hydraulic potential
energy, lead acid batteries, lithium ion batteries & mass heat sinks work well.