You have to be careful about the distinction between "resolution" and "accuracy": there are a couple of chips that I know of (the TC77 and DS1631) that provide readings down to a 16th of a degree C, but the datasheets say they can have an error of +- a whole degree. So you can get very accurate relative
measurements (i.e., "The room is an eighth of a degree warmer than it was 10 minutes ago"), but the absolute
value could be off (i.e., it might be telling you the temperature is 17.125 degrees C when it's actually 16.875).
The TC77 is available inexpensively from Mouser (and probably Digi-Key and others, but I happened to be ordering from Mouser when I decided to buy a few). I have a couple dozen DS1631s that I bought last month with a plan to mount them to DIP adapter boards for people who don't do SMD soldering (much like Sparkfun and NKC do for other sensors). If you want to help get me off my butt and doing
that by being my first customer, send me a PM or email, and we may both benefit