Actually, no, because the glass braid insulation would melt before then (900 ºF).

For people that will be reading this in the future... Do not shorten the wire! It may drastically decrease accuracy. Please look up how thermocouples work before using one. I also recommend using a T-type instead, unless you need to measure extremely hot stuff.

Assuming you're using their built-in ADCs, do they have the same reference voltage? I don't remember if the ATmega328P has configurable internal reference voltage. Even if not, maybe one of them has a bad voltage reference circuit. Maybe also try using external reference voltage via the Aref pin—though I don't know if the LilyPad breaks that out.

You sure can, but the data will not be reliable since the reading may vary by (at least) 2-3 C, which is a substantial amount when it comes to human body temperature.

yeah sorry i made a general post- look below!

yeah just use the thermocouple- the mfg has specific requirements it has to meet (EMF- eletro-motive force) (k cant vary more than .089mv from 200-500F)there are 32 mv/degree

if you are super concerned- look for a special limits sensor- it will cost a bit more but it is only allowed .044mv from 200-500

at 2501F you are going to need a very very expensive thermocouple- a type R/B to get those very high temps-

the thermocouple needs to be the only thing exposed-after you use it you can slide it in a little further and it will maintain its accuracy

This is a k rated sensor, however the probe tip is a tiny affair, it's the bit on the end of the insulation. On kiln temp sensors the tip is several inches long, this allows it to be inserted through the kiln wall without exposing the insulation to excessive heat.
You can find ones designed for kilns by searching "k temperature probe" on google

The short answer is probaly cost. The sensor functions at 2500 degrees but the materials may nit last long at high temperatures. Tcs made for that type of enviromemt are sheathed in high performance alloys. Most people won't need that. For your application checkout omega.com, there website is not very good so you may want to call.

Not sure if this is going to be much help.
Many years ago I worked at a metallurgical test lab. They basically tested samples of metal under high tensional stress along with high temperature. There was a guy whose sole job was building thermocouples that would sit inside a furnace to measure the temperature of the specimen under test.
He would take two pieces of dissimilar wire and spot weld them at one end to form the hot junction. To insulate the two pieces of wire from each other and from the outside world, he would thread ceramic beads onto the two wires.
Each ceramic bead was cylinder shaped, about 6mm in height and about 4mm in diameter. There were two small holes running through the cylinder.
The finished thermocouple was very fragile and needed great care during installation. It resembled a necklace of pearls. The goal though was that it could stand extremely high temperatures and was somewhat flexible for routing out of the furnace.
I'm afraid that I have no idea where to source the ceramic beads, or the bare al/ch wire to make a K thermocouple from scratch.

Ditto to this question!

Stainless is a terrible conductor of heat. Epoxying this inside a SS tube would effective be insulating it from whatever you're trying to measure.