Helping people with computers... one answer at a time.
Guaranteed? Certainly not. Unlikely, perhaps, but there are definitely ways that the conversation could still be around, though likely only for a short time.
We'll start with the obvious: the person you were conversing with could have a complete history of the conversation on their side. There's no way to know if the person you are IMing with is recording the entire conversation. They certainly could be, and you can't do anything about it.
Spyware, keystroke loggers or parental monitoring software can most definitely keep track of you IM conversations. Some may keep the log hidden somewhere on your machine, others may in fact send the conversation to some other computer. Aside from running regular, and updated, anti-spyware software, there's once again little to be done here.
And finally, like any program run under Windows, IM programs use memory, and that memory can be swapped out to disk and end up in the paging or swap file. There's a small chance that your conversation, or parts of it, could reside there for short amounts of time. Windows goes through great lengths to keep the paging file secure, however, quoting a Microsoft web site: "The file system security for paging files prevents any user from gaining access to and reading these files, and these security settings cannot be changed. However, someone other than the authorized user might start the computer under a different operating system to read a paging file."
What this means is that with a lot of work, and a lot of luck, someone who has physical access to your machine might be able to extract some data from the paging file.
But it's pretty darned difficult and unlikely. I'd be much more concerned about the person I'm chatting with, and spyware, myself.