To give you an alternative for the sensor:
http://shop.boxtec.ch/product_info.php/cPath/39_71/products_id/40658
This one offers you medical accuracy (at least in the temperature window of a human body), is read using I2C (you don't have to twiddle with amps and the like, everything included) and is quite focussed (5°). I use it for something similar, although I use it only for a momentary measurement, not for constant wearing.
With a clever programming (longer sleep periods) you should be able to drive it from a not to big battery together with a minimal arduino setup (an ATtiny might be enough).