If you're already good with math and need some help with a mathematical model of a heat exchanger, check out a copy of this book:
Amazon.com: Introduction To Heat Transfer (9780471386490): Frank P. Incropera, David P. DeWitt: Books
I keep one on my bookshelf.
For loads that will last 15-20 minutes, don't bother trying to store heat. You need a heat exchanger that will get rid of it as fast as you produce it. There are enough numbers in the above post (except diesel engine efficiency - conservatively suppose 50% of the energy going in needs to leave through the radiator, and the rest through the output shaft and tailpipe) to calculate the total amount of heat you need to dissipate.
Given initial temperature and flow rate for air and water (or oil), you should have enough information to guesstimate heat flux per square meter of heat exchanger. I say guesstimate, because fins complicate things a great deal.
Maybe once you compile the above information, you could e-mail it to a company that makes custom radiators and ask them to size you one. I bet they have a spreadsheet for their radiators that's more accurate than anything I could spit out by guessing at the fin effectiveness.