Options for heating

Heating will still be necessary, especially for those areas that will be experiencing the enhanced pendulum swings of extreme heat and extreme cold.

Mitigation needs to be considered.  Structures that are earth bermed or underground use the surrounding earth as insulation. Applied structural insulation as determined by R factors help to temper the comfort level. Occupants may also need to wear additional layers of clothing to handle extreme peaks. Points of entry and exit should have a second "air lock" door to minimize the lost of already heated air in a structure.

Solar devices for both active and passive heat transfer, where appropriate, can provide the needed level of heat. 

If enough electricity is available, there are many clean methods to use it to heat. Wire elements, ceramic elements and heat pumps are all options.

Then we have the original active method of heating.  Fire.

Fireplaces, stoves, furnaces, central boilers. They mark the standard for most of human history. Today they are still in use. In trying to keep carbon and toxic gas emissions to a minimum new designs and technology need to be introduced.

Mass heaters. Taking the heat from a fire and the smoke if possible to heat a thermal mass. Bricks, stone, sand, to a lesser extent water. They then can radiate heat for a long time after the fire is out. 

Rocket Stove. The Native American prairie stove, designed to take the prevailing wind to drive a small fire to produce enough heat to even burn it's own combustibles. This was the start of the rocket stoves and they have been in the forefront of innovation lately. First with camping, and now being experimented with for homes. One commercial version fire pit had proved itself very popular and may help to advance the technology.