SUPER-DUPER SENSITIVE THERMOMETER?

Hi, I am a doing an electrical project, and I need a verrrry sensitive thermometer. I know that there are some out there that will give you a reading to the "tenths" of a degree, but I am looking for something that will work in the "hundredths" of a degree or even "thousandths of a degree". Do they make thermometers this sensitive? This electrical project that I am working on demands extreme temperature reading accuracy, to prevent temperature overload! In other words, the whole thing goes "kapooey", and I am stuck with a bunch of melted resistors! Thanks for the help, and I do give quick points for the best answer!