From the Model Mayhem FAQ:

How do I find messages I've sent to other people or that they've sent to me?
There are two ways you can find messages you've sent and received from others:

#1 - Type in part or all of their display name or Model Mayhem account number into the search box in your inbox. The messages between you and that member should appear as a result:

#2 - Go to that person's profile and click the Message History button. This will populate the search for you! It looks like this: