The best thing to do would be to get consoled in before this happens and try to monitor from there. I don't know the command off the top of my head, but ideally you should be able to do a show cpu or something to see the percentage (and also run what ever commands gets you a list of all the processess).
Ideally, if you are already consoled in before the CPU spike, you may be able to get some information (although I've seen it take awhile to process and return what you are asking for).
I'm working a similar issue right now, that I think we've identified the problem. Please let me know if you've been able to catch the cpu process causing the issue.
(you might want to make sure you configure the CLI session timeout to be something higher than the default 5 minutes... try "config session timeout 120", I know this works for SSH sessions so hopefully it changes the console as well)