> I would have thought anything that can radiate heat slowly and consistently would by necessity also absorb heat slowly and consistently
Aside from the technological measures mentioned in other replies, I'm not sure this follows. Thermal energy transfer is proportional to the temperature difference. So a high thermal mass storage can absorb energy quickly from a high temperature source, experience a small change in temperature, then expel the heat slowly into a sink slightly cooler than itself. That is a gross oversimplification but it at least it shows that the effect is not too surprising.
Aside from the technological measures mentioned in other replies, I'm not sure this follows. Thermal energy transfer is proportional to the temperature difference. So a high thermal mass storage can absorb energy quickly from a high temperature source, experience a small change in temperature, then expel the heat slowly into a sink slightly cooler than itself. That is a gross oversimplification but it at least it shows that the effect is not too surprising.