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The Carnot limit

No heat pump can be better than an ideal Carnot machine between the same temperatures. The limit depends only on the temperatures in kelvin. The smaller the temperature difference, the higher the COP can be.

COPHP,max=THTH−TCCOP_{HP,max} = \frac{T_H}{T_H - T_C}highest possible heating COP
COPR,max=TCTH−TCCOP_{R,max} = \frac{T_C}{T_H - T_C}highest possible cooling COP

Symbols

THT_Hhot temperatureK
TCT_Ccold temperatureK

Example

Inside 20 °C (293 K), outside 0 °C (273 K):

COPmax=293/20≈14.7COP_{max} = 293/20 \approx 14.7. Real heat pumps are often around 3–4.

Always use kelvin. With degrees Celsius the answer is completely wrong.
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Part of Thermodynamics: Heat pumps and refrigeration.