What is the common name for the colder reservoir in a heat engine?

The common name for the colder reservoir in a heat engine is the heat sink.

A heat engine operates between a hot reservoir and a cold reservoir. It absorbs heat from the high-temperature source, converts part of that energy into useful work, and rejects the remainder to the colder heat sink. The sink is called a “sink” because it receives waste heat rather than supplying the engine’s main energy input.

This arrangement explains why no heat engine can turn all incoming heat into work. After a complete cycle, the working substance returns to its starting state, but some heat must still be discharged to the cold sink. The ideal Carnot efficiency is η = 1 − T_c/T_h, so a colder sink permits a higher theoretical efficiency when the source temperature is fixed.

The heat sink is not the same thing as the working fluid. The working fluid—often a gas, vapor, or liquid—undergoes the cycle and transfers energy between the reservoirs. In a refrigerator or heat pump, the roles are operated in reverse: work is supplied to move heat from the cold side to the warmer surroundings.