Sounds like your app has some infinite loops in it. The best way to find such loops is to take multiple thread dumps a few seconds apart and then look for threads that are busy and appear to be in the same code. Then look at the stack trace for your code and examine that code to find out why it is in a loop.

You should have a look to the JVM Garbage collection.

see [1] for JDK5. Often the GC goes crazy if you reach a load threshold.

Look whether something special is around this time.

Also it might be a memory leak, the heap is mostly used and there is not enough space to create new objects. You might check the VM from time to time with 'jstat' it is included in the java installation since 1.5

[1] http://java.sun.com/docs/hotspot/gc5.0/gc_tuning_5.html

See if this helps:

http://www.crazysquirrel.com/computing/java/basics/java-thread-dump.jspx

And yes your results will be much better if you do this then you hit 300% CPU usage! ;-)

See the GC article, you can activate the GC.logging in production (I've done it long time) it is not a visibly impact and give hints about the memory ussage in such cases.

jstat can be used to have a quick view of the heap allocation and gc activity (jconsole and visualvm might  not aceptable in production)

Sending a QUIT signal will not kill the process, only cause a thread dump. Don't you have stdout redirected to a file? If so, the thread dump will show up there. And yes, jstack will also get the thread dump.