Perhaps you need an explanation "from the horses mouth" - i.e. GaJ himself! There is a recent thread on the BF forums about the chat files.
But my non technical explanation, FWIW, is that usually the definitive chat files are sent / stored only in the relevant dropbox folder - you can see from there what is present / how big a file(s) it is. The temporary files created as the chat files are made are deleted automatically.
The problem was a bug that arose when GaJ changed the format of the chat messages (at around v 2.9 I think), so that the new and old versions of chat could not "chat" with each other. If two people with incompatible versions then tried to chat, the temporary files that were created as part of the process were not then removed automatically, as they normally are: I guess because the chat didn't actually complete correctly.
Those temporary files were created - and remained - in whichever place Windows puts temporary files. (AFAIK, not a problem for the Mac version, which I use.)
Hope this helps.