The general idea is that you don't use possessives when referring to an entity already defined. In a linguistic sense, these can be thought of as phrasal proper nouns.

A made-up example:

Let $T_H$ be the heater temperature.

We know that the heater temperature is greater than ambient.

Therefore, the heater temperature is guaranteed to be greater than any heater's temperature that is cooler than ambient. (The temperature of the heater in question is guaranteed to be lower than the temperature of any other heater, if that heater is cooler than the ambient temperature).

The general idea is that you don't use possessives when referring to an entity already defined. In a linguistic sense, these can be thought of as phrasal proper nouns.

A made-up example:

Let $T_H$ be the heater temperature.

We know that the heater temperature is greater than ambient.

Therefore, the heater temperature is guaranteed to be greater than any heater's temperature that is cooler than ambient. (The temperature of the heater in question is guaranteed to be lower than the temperature of any other heater, if that other heater is cooler than the ambient temperature).