Since upgrading to 4.1 I've had to clear out my MT directory daily, as core.xxxx (numbers) files keep being created at about 15MB until my disk space is full.

I've read other threads that address what these core files are: http://forums.sixapart.com/index.php?showtopic=53104

However, I have not found a thread that deal with these being created at excessive amounts.

I would appreciate any tips to troubleshoot this issue. For now, I have disabled all plugins to see if it is related to them.

First things to do is have a look in your server logs, see if there are any clues there.