One of these summers on a really, really hot day, Eversource might present its customers with an odd-sounding proposal: Let us make your house warmer.

The state’s largest electric utility is seeking permission in New Hampshire and its other New England markets to raise the temperature on some home air conditioners by several degrees, reducing the amount of electricity being consumed during periods of peak usage, such as a hot summer afternoon.

The idea is being discussed at the Public Utilities Commission as part of various energy efficiency proposals. Details are very much up in the air and no timetable has been set.

Eversource would like to sign up a few thousand New Hampshire homeowners who have WiFi-enabled “smart thermostats” and who, in return for payments, will give the utility permission to have the thermostat company raise the temperature a few degrees a certain number of times each summer. These customers would be able to opt out of the change at specific times, although that could lower the amount of payment.

“Raising it a couple of degrees, no more than 4 degrees, is usually the optimal amount … to get a benefit without affecting the customer too much. The hope is that customers don’t even know,” said Michael Goldman, manager of regulatory planning and evaluation for Eversource.

This idea is an example of what is known as demand response, or giving customers information so they can cut their demand for electricity when requested.

Demand response programs exist for customers such as factories or large stores, which shut off machinery or dim lights on request in return for payments or a lower electricity rate. It has already become an important part of the whole power system. ISO-New England, which runs the six-state power grid, includes 2,700 megawatts of demand response and targeted energy efficiency in its calculations about future power availability. That figure is about 7 percent of the region’s total power needs and is equal to about twice the output of Seabrook Station nuclear power plant.

Eversource’s proposal would be one of the first opportunities for homeowners to participate in a demand response program in New Hampshire.

The utility is interested because “peak shaving,” or reducing a bit of little electricity usage during peak times, can save a huge amount of money because of the way electricity markets are structured.

Green Mountain Power in Vermont, for example, says that integrating some home batteries allowed it to shave enough peak electricity demand last summer that the utility saved more than half a million dollars because it had to buy less very expensive peak power. Liberty Utilities is rolling out a similar program as a pilot for some of its electric customers in New Hampshire.

“What we’re trying to achieve is potentially flattening peak load,” said Goldman. “These peak times are responsible for driving … some very expensive investment. If we can drive down peak load during a limited number of hours, we can have a disproportionate effect on costs.”

Goldman noted that a number of peak-shaving programs are being studied or in pilot programs in Massachusetts, involving such things as changing the temperature on water heaters to store energy when electricity is cheap and use it when electricity is expensive.

“There is thermal storage, battery storage, types of load management, which is ultimately where I think this is headed more generally,” he said.

All these are examples of how the power grid is changing in response to technology such as distributed solar panels and intermittent wind power, as well as concerns about climate change that are closing down older power plants, especially those burning coal and oil. The nation’s huge growth in natural gas production is also roiling the mix.

Under the old model of the electric grid, a relatively small number of large power plants produce all the electricity that all their customers need at any given moment. The new model is a much more complex two-way interaction between customers and producers that seeks to shape demand so that it can be met with the least pollution and cost possible.