A heat storm, as defined by the California Energy Commission, is what most would refer to as a heat wave. According to the commission website, heat storms occur when the temperature reaches 100°F (38°C) for three or more consecutive days over a wide area (tens of thousands of square miles).
Normal hot temperatures cause electricity demand to increase during the peak summertime hours of 4 to 7 p.m. when air conditioners are straining to overcome the heat. If a hot spell extends to three days or more, however, nighttime temperatures do not cool down, and the thermal mass in homes and buildings retains the heat from previous days. This heat build-up causes air conditioners to turn on earlier and to stay on later in the day. As a result, available electricity supplies are challenged during a higher, wider, peak electricity consumption period.
The term "heat storm" is generally unknown outside of California and Texas, and even within the state the term heat wave is often used instead.