I have to find a memory leak in a Java application. I have some experience with this but would like advice on a methodology/strategy for this. Any reference and advice is welcome.

About our situation:

1. Heap dumps are larger than 1 GB
2. We have heap dumps from 5 occasions.
3. We don't have any test case to provoke this. It only happens in the (massive) system test environment after at least a weeks usage.
4. The system is built on a internally developed legacy framework with so many design flaws that they are impossible to count them all.
5. Nobody understands the framework in depth. It has been transfered to one guy in India who barely keeps up with answering e-mails.
6. We have done snapshot heap dumps over time and concluded that there is not a single component increasing over time. It is everything that grows slowly.
7. The above points us in the direction that it is the frameworks homegrown ORM system that increases its usage without limits. (This system maps objects to files?! So not really a ORM)

Question: What is the methodology that helped you succeed with hunting down leaks in a enterprise scale application?