What if winter were much colder?

In winter, a heater keeps a house warm. On a very cold day, the heater runs more.

What if winter got much, much colder? How much more heat would a house need?

On a mild winter day, the heater in your home might click on now and then. On a bitterly cold day, it seems to run and run. Is that just a feeling, or does colder weather really mean much more heating?

In this lab, a house is kept at a cozy 20 °C. Outside, it starts at 0 °C, freezing point. What happens to the heat the house needs if winter turns much colder, all the way down to −20 °C?

A heated building in winter must replace the heat lost through its envelope. That loss depends on the envelope's insulation (its U-value), its area, and the difference between indoor and outdoor temperatures.

This lab holds the thermostat at 20 °C and lowers the outdoor temperature from 0 °C to −20 °C. It asks how the heat loss, the heater's running time and the daily heat demand respond, and what happens when the heater's own limit is reached.

Outside it is freezing, 0 degrees. Inside it is 20 degrees.

The heater turns on and off. It keeps the house warm all day.

On a 0 °C day, our insulated model house leaks heat at about 3.6 kilowatts. Its 10-kilowatt heater easily keeps up, running only about a third of the time to hold 20 °C.

Over a whole day, the heater puts in about 86 kilowatt-hours of heat. A kilowatt-hour is the energy a 1-kilowatt heater uses in one hour, so that is like running a 1-kilowatt heater for 86 hours.

With U = 0.6 W/m²·K and A = 300 m², the shell's conductance is 180 W/K. At ΔT = 20 K, Q = 3.6 kW; the 10 kW heater runs 36% of the time and delivers 86.4 kWh per day.

The model assumes a constant outdoor temperature, no air leaks or ventilation, and no heat from the sun, people or appliances, so this is a clean test of the temperature difference alone.

Now Olly makes it much colder outside: 20 degrees below zero!

Warmth rushes out twice as fast. The heater has to run much longer.

Set the outside temperature to −10 °C. The gap between inside and outside grows from 20 to 30 degrees, and the heat loss grows to about 5.4 kilowatts. Now try −20 °C: the gap is 40 degrees, twice as big as before, and so is the loss, about 7.2 kilowatts.

The heater now runs about 72% of the time, and the house needs about 173 kilowatt-hours of heat a day, twice the 0 °C day. Twice the temperature gap means twice the heat.

Q is linear in ΔT: 3.6 kW at 20 K, 5.4 kW at 30 K and 7.2 kW at 40 K. The heater's duty cycle rises from 36% to 54% to 72%, and daily heat from 86.4 to 129.6 to 172.8 kWh.

The insulated house never runs out of heater on this slider: even at −20 °C, the 'warmest the heater could manage' readout is 35.6 °C. Switch to a leakier house (U = 1.5) and the same heater reaches its limit near −2 °C. At −10 °C it can only hold 12.2 °C, and at −20 °C just 2.2 °C, running flat out.

Heat flows from warm places to cold places.

The bigger the difference, the faster it flows. A colder outside means a bigger difference.

Heat moves through a wall at a rate that depends on how leaky the wall is, how big it is, and how much warmer one side is than the other. Double the difference and you double the flow.

That is why the important number is not the outside temperature itself, but how far it is below the inside temperature. Going from 0 °C to −20 °C does not just add a little: it doubles the gap from 20 to 40 degrees.

Fourier's law of conduction gives a heat flow through a slab proportional to its area and the temperature difference across it, divided by its thickness (OpenStax §14.5). Summed over a building, this gives Q = U·A·ΔT, with all envelope properties folded into U·A.

Two consequences follow. Heating energy scales with the time-integrated temperature deficit below the indoor setting, and a fixed-size heater imposes a ceiling, T_max = T_out + P ÷ (U·A). The model's limits: real houses also lose heat through air leaks, real weather changes hour by hour, and sunshine and occupants add heat the model ignores.

Scientists keep count of how cold each day is.

Colder days mean homes need more heating. In the United States, homes in colder parts use more energy on average.

The U.S. Energy Information Administration (EIA) measures cold with heating degree days. Take a day's average temperature and see how far it falls below 65 °F. A day averaging 29 °F counts as 36 heating degree days. The more of them, the more heating homes need.

The EIA reported that a typical January in the United States has about 831 heating degree days, but January 2025 had 927, about 12 percent more. It also notes that homes in the Northeast and Midwest use more energy on average than homes in the South and West, because they need more space heating.

EIA defines heating degree days as the base temperature (65 °F in the United States) minus a day's mean temperature, and uses population-weighted HDDs as an indicator of heating demand. In February 2025 it reported that January 2025 had 927 population-weighted HDDs against a typical 831 (the previous 10 Januarys' average), and that the cold raised consumption.

The degree-day method rests on the same linear relationship as this model: heating need grows with the temperature deficit. EIA also attributes higher average household energy use in the Northeast and Midwest to their higher space-heating demand.