Myself and a few others do this quite a bit, and there's a good bit of gathered info on doing just that.
Read through this link: http://www.homebrewtalk.com/f36/over...y-cool-295579/
I have made some wonderful brews using this technique, I suggest you give it a try!
Edit: I'm assuming that you start your mash at a conversion temp, then let the mash sit overnight. Or do you mean just literally dough in at room temp? If the latter is the case, I agree with the previous posters, you probably wont get any conversion.