The total heat load needs to be considered, which for a dual pressurized seal is inboard seal face generated heat + outboard seal face generated heat + heat soak; you can incorporate churning effects too if you have a larger seal, but typically churning heat can be neglected. On the unpressurized arrangement, the total heat load is usually the sum of the inboard and outboard seal face generated loads; the amount of soak, if any, will be minimal. Ultimately the magnitude of the heat load and subsequent cooling flow rate required comes down to the amount of heat soak - seals in higher temperature processes with dual pressurized seals will require a fairly substantial flow rate for cooling. This gets triggered by whether or not your reservoir or system is being cooled, which is when the heat soak becomes a factor - especially in a dual pressurized arrangement.