Today, that is not the issue, it is the exact opposite. We are seeing prolonged heat emergencies across much of the Southern and Eastern portions of the country. The dominance of air conditioning in this era of "comfort" and the new demands of computer server farms also drawing power that was not needed previously will cause a significant balancing act of meeting the demand with power generation and transmission.
I've never seen it personally, but high-voltage power lines can sag when there are large power demands and electricity being transmitted. Besides the heat itself, the risk comes from wildland fires damaging power poles and lines, taking systems offline when the power demand is high, such as it is today in California.
I would not be surprised to at a minimum hear of spot outages due to the heat emergency and perhaps a collapse of one or more systems from being overloaded with demand. I anticipate that power companies will be asking customers to unplug anything drawing electrical power that is not essential, in order to lower the demand.