What if a house’s heating switched off on a cold night?

It is a freezing night. Inside, the house is warm and cozy. A heater keeps it that way.

What if the heater stopped? Would the house get cold right away?

On a winter night, warmth is always slipping out of a house through its walls, roof, windows and floor. Usually a heater puts the warmth back as fast as it escapes, so you never notice.

But heating can stop: a furnace can break down, or a storm can cut the power. In this lab, a house at 20 °C sits in a steady 0 °C night, and the heater switches off. Does the house turn cold in minutes, in hours or in days? And does it cool at a steady rate?

A heated house in winter is in a steady state: heater output equals the heat lost through its envelope. Remove the heater and the house runs on stored heat, the energy held in its air, walls, floors and furniture.

This lab models a house with a 300 m² shell, an average U-value of 0.6 W/m²·K and a heat store of 25 MJ/K, held at 20 °C until its 10 kW heater stops on a night that stays at 0 °C. The question: how does its temperature evolve over the next 48 hours?

With the heater working, the house stays at 20 degrees.

Warmth leaks out all the time. The heater keeps putting it back.

With the heater working, our model house loses heat at about 3.6 kilowatts, all night long. The 10-kilowatt heater switches on and off to hold 20 °C, running about a third of the time.

The house also stores a lot of heat in its air, walls and floors. The model treats it like a giant hot-water bottle holding as much heat as about 6 tonnes of water. That stored heat is what keeps the house warm for a while after the heater stops.

At 20 K of difference, the shell loses Q = U·A·ΔT = 0.6 × 300 × 20 = 3.6 kW, so the 10 kW heater runs 36% of the time. The model lumps the whole house into one heat store, C = 25 MJ/K, comparable to about 6 tonnes of water.

Dividing the store by the shell's conductance gives the time constant τ = C ÷ (U·A) = 25,000,000 ÷ 180 s ≈ 38.6 hours. It sets how quickly the house would cool if the heat input stopped.

Now the heater stops. The house starts to cool down.

At first it cools quite fast. Later it cools more and more slowly.

Choose 'power cut' and press play. In the first two hours, the house drops about 1 °C. After 12 hours, a long winter night, it is down to about 15 °C. After a whole day it is about 11 °C, and after two days about 6 °C.

Look at the graph: the line curves. In the first 12 hours the house loses about 5 degrees, but between hours 36 and 48 it loses only about 2. It never quite reaches 0 °C, it just creeps closer and closer.

With P = 0, C·dT/dt = −U·A·(T − T_out), so T − T_out = 20 · e^(−t/τ). The model's run gives 19.0 °C at 2 h, 14.7 °C at 12 h, 10.7 °C at 24 h and 5.8 °C at 48 h. After one time constant (38.6 h) the gap has shrunk by 63%.

The heat loss is proportional to the remaining gap, so it starts at 3.6 kW and shrinks as the house cools. Change U to compare: with no insulation (U = 2), τ = 11.6 h and the house is at 7.1 °C after 12 h; well insulated (U = 0.3), τ = 77.2 h and it is still 17.1 °C.

Heat moves from warm places to cold places. A big difference makes it move fast.

As the house gets cooler, the difference gets smaller. So the heat leaks out more slowly.

Heat leaks out faster when the inside is much warmer than the outside. At first, the house is 20 degrees warmer than the night, so heat pours out. As it cools, the difference shrinks, so the leak slows down.

In the model, two things slow the cooling: insulation, which slows the leak, and a bigger heat store, which has more warmth to lose. Our model is simple. It gives the whole house one temperature, keeps the night at exactly 0 °C, and leaves out drafts, sunshine, and the warmth that people and appliances give off.

Because heat loss is proportional to ΔT, the decay is exponential, the same mathematics as Newton's law of cooling for a cup of cocoa. The time constant τ = C ÷ (U·A) grows with thermal mass and shrinks with leakier or larger envelopes.

The model's assumptions are strong: one lumped temperature for every room, wall and floor; no air leakage or ventilation; no solar or internal gains; and an outdoor temperature that never changes. Each of these is a real heat flow or a real variation that the single equation leaves out, so its numbers show the shape of the cooling, not a forecast for any real house.

Big winter storms can sometimes stop the heating or the power.

Families can get supplies and flashlights ready. If it gets very cold, people can go to warm places that have power.

Ready.gov, the U.S. government's preparedness website, says a winter storm can last a few hours or several days and can cut off heat and power. It suggests gathering supplies in case you need to stay home for several days without power, with extra batteries for flashlights. If the cold is extreme, it suggests going to a community location that has power, and checking with local officials about warming locations nearby.

It also gives one important safety rule. Never heat a home with a gas stove or oven, and use generators and grills only outdoors, away from windows. They can fill a house with a poisonous gas called carbon monoxide.

Ready.gov (FEMA) notes that winter storms can last from hours to days and cut off heat, power and communications, and that older adults, children, sick people and pets are at greater risk. During an outage it advises going to a community location with power if heat or cold is extreme, and checking with local officials for warming and cooling locations.

Its carbon monoxide guidance is firm: generators, camp stoves and charcoal grills only outdoors and at least 20 feet from windows, never a gas stovetop or oven to heat a home, and battery-backed CO detectors on every level. The model's lesson fits the advice: insulation and stored heat buy time, but not unlimited time.