I'm not sure if it's the same model or not but I do know one of the imac models had a problem with over-heating.

Try these things:

1. SAFE Boot & Repair Permissions. After repairing permissions then reboot normally.

2. Delete your LW prefs folder whilst it is CLOSED; it is found here /Users/your_username/Library/Preferences/LimeWire

3. Consider doing this Tip: Purge the Downloads Queue!

4. Don't share over 1,500 files as mac osx's java doesn't handle it very well.

5. Make sure your system is using Java 1.5 by going to Utilities folder, finding Java folder, preferences, ... explained here Setting up Java 1.5 But do this whilst LW is closed.