In Plan 23, who normally dictates the cooling water requirements such flow, temp, pressure. Is it the supplier or is there also a section on API 682 where it dictates the CW requirements?
API 682 doesn't spec parameters like flow rate, pressure, or temperature but it does give general guidelines. For instance, Plan 23 is generally the plan of choice for boiler feed water pumps and services where the product viscosity is low. My guess is the OEMs would be able to give a recommendation. Plan 23 can be tricky because if your cooling water is significantly cooler than your process, you'll have significant heat soak, which can result in fouling of your heat exchanger. It is their task to figure that out, but it doesn't hurt to check their work. Their is a paper by Tom Arnold and Chris Fone about mechanical seal performance calcs, it provides useful guidelines for estimating seal performance. Look it up if you're interested!
You could always look at a hi-temp type of seal with lube groove faces. I have them installed with many of my customers on Boiler Feed applications, no cooling required up to 330F.