Hmm, found the answer on another website and this does seem to work. We are now asking the JVM to make a heap dump when it encounters an OutOfMemoryError with the following options:
-XX:+HeapDumpOnOutOfMemoryError -XX:HeapDumpPath=./java_pid<pid>.hprof
As found on:
http://www.oracle.com/technetwork/java/javase/tech/vmoptions-jsp-140102.html