Just think of the effects of moving heat from inside 100s of millions of Americans homes to the outside.
Here I'll do it for you.
Here's the step-by-step reasoning and calculation using real-world data:
1. Key Assumptions and Data
Number of US households: ~130–132 million (using ~130 million).
AC electricity use: Total US residential AC ~254 billion kWh/year (2020 data); average ~1,900–2,000 kWh per household/year for cooling.
Air conditioner COP (Coefficient of Performance): Typically 3–4 (meaning for every 1 unit of electricity, it moves 3–4 units of heat from inside to outside). Use 3.5 as average.
Net heat added to the environment: The heat pumped from indoors (which would eventually leak out anyway) + all the electrical energy consumed (which fully becomes waste heat outdoors via the condenser and inefficiencies). Net addition ≈ total electricity used (the "moved" heat is neutral in the long run for the planet as a whole).
Earth's atmosphere: Mass ≈ 5.15 × 10¹⁸ kg. Specific heat capacity of air ≈ 1,005 J/(kg·K).
Total US AC electricity: ~254 × 10⁹ kWh/year.
Convert to Joules: 1 kWh = 3.6 × 10⁶ J → ~9.14 × 10¹⁷ J/year.
With COP ~3.5, the gross heat dumped outside is higher (~3.5× the removed indoor heat + electricity), but net planetary addition is just the electricity input (the rest is relocation). So we use ~9.14 × 10¹⁷ J as the effective added energy.
The formula for ΔT (temperature change) is:
ΔT = Q / (m × c_p)
Where:
Q = total heat energy added (J)
m = atmospheric mass (5.15 × 10¹⁸ kg)
c_p = specific heat (~1,005 J/kg/K)
ΔT ≈ 9.14 × 10¹⁷ / (5.15 × 10¹⁸ × 1,005) ≈ 1.77 × 10^{-4} K (or ~0.000177 °C) per year if all that heat were magically added uniformly and stayed in the atmosphere without any dissipation, radiation to space, ocean absorption, etc.
The net global temperature change from this is effectively zero on any meaningful scale—far smaller than 0.000000001°C (or 10^{-9} °C).
