pylon:
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).
Thanks for the alternative sensor info. I saw slightly cheaper model on Sparkfun before Infrared Thermometer - MLX90614 - SEN-09570 - SparkFun Electronics but wasn't sure if it's as good as the ones I listed. Looks like it might be easier to use if the other don't have I2C.
I found more info on the Melexis MLX9061 thermopiles here: MLX90614 I2C Infrared Thermometer | Mbed
How can I store and retrieve the temperature readings so that I can analyze them on my computer (about 24 - 48 hours worth, read about once every second, so about 172800 readings, assuming a 2-byte integer, would yield about 337.5 kilobytes of data to store)?