API Plan 23 is circulation of the fluid in the stuffing box through a heat exchanger back into the stuffing box. The fluid in the stuffing box is the process fluid. Even with the throat bushing required for this plan to work, you'd end up using the process fluid. Whatever you attempted to fill the stuffing box with would leak into the volute.
Any time you want to use a fluid in a mechanical seal application for pressurization of the space between a tandem/dual or, back to back/double seal (API 52, 53, or 54), or as a clean and cool fluid to flush the seal (Plan 32) you need to choose something that is compatible with the process. Somehow, somewhere your friends in production will want to get this Dowtherm, diesel, water, methanol, oil, whatever it is, out of their process.
For API 32 (external flush stream) you want to use a clean, cool fluid to flush the seal. It is best if this fluid is a component of the process or can easily be removed. Cost is also an issue to consider. In an oil refinery Coker Unit there are many pumps moving hot sludgy fluids that set up as they cool. It would be fantastic to flush these seals with diesel because it is clean, compatible with the process, and readily available. Tell the unit manager that he needs to dump 5 gpm (2.5 gpm for each seal on a between bearing charge pump) into each pump to keep the seals working…. Watch how fast he puts packing into the pump. Refined diesel sells for, what, $1.30 or so a gallon?
Flush plans like plans 52 or 53 (unpressurized or pressurized circulated seal fluid) require fluids that will lubricate the seal faces, have good heat transfer properties, are compatible with the process, won’t foam at operating pressures, and again, are inexpensive. These flush plans require that the fluid remove the heat generated at the seal faces as well as lubricate at least one set of seal faces. Even with a plan 52 expect that some seal buffer fluid will one day leak into the process. Again, cost is an issue. Ideally the seal reservoir is drained after each seal failure, then cleaned and refilled prior to start-up. Imagine spending $2,100 on buffer fluid each time a pump seal failed.
I am sure that your local seal vendor can help you choose a flush plan that is best suited for your application. Don't forget to ask about installation requirements. Some of the flush plans listed above will require thermal cycling or specific equipment installation methods to increase the plan's efficiency.