The cost is a function of the size and mass. So, more heat capacity and less mass means lower cost per mwh.

These things are extremely simple and fairly efficient. It's resistive heating (wires and spools) of a thermal mass (sand/stone) in some kind of container (a simple silo) with a lot of insulation and some pipes to heat up water. Higher temperatures mean getting the heat out is easier and that the battery will work for longer. Basically until the temperature drops below the required temperature.