I've been obsessed, mildly, with Feolite. It could be brought back for these sorts of applications to great effect. It's got the volumetric heat capacity of water and the ability to withstand much greater temperatures without any annoying phase transitions. It was very popular in the UK, where they went in early on charging for electricity on a rate varying by hour. The basic formula is easy, but there's a lot of secret ingredients to get the heat capacity way, way up.

Speaking of home uses and phase transitions, they have made inroads into making materials with a phase transitioned tuned to household temperatures. Say you have aimed for seventy-two Fahrenheit. The temperature gets higher than that? The material melts, absorbing ambient heat. Then, as the temperature dips below seventy-two Fahrenheit, it freezes, releasing heat. It would make a fantastic sort of "heat capacitor," designed to deal with rapid, small-scale temperature fluctuations, while larger heat batteries could deal with fluctuations over days, weeks, and so on.

Only problem is that these phase transition materials tend to be terrifyingly flammable, so far. Like soaking all of your drywall panels in candle wax before putting them up.