As said above, I wouldn't use thermocouples for this. They are meant for much wider temperature ranges. Getting +/-0.1°C is next to impossible. At least not without fancy signal conditioning and heavy calibration.
Another thought, they would probably require proper encapsulation for this application.
Medical thermometers are cheap these days and AFAIK, there is no shortage as of yet? Why bother?
But yeah, the most common approach these days seems to be IR thermometers, so if you want to design one, that's probably what you should look into.