A thermocouple produces a very small voltage per degree at EVERY junction.
That INCLUDES the connections to its leads.
For this reason, a SPECIAL type of amplifier (thermocouple amplifier) is required. There are many different types, of which two are mentioned above.
They amplify the signal to a voltage large enough to be read by a PICAXE but just as importantly, they compensate for the voltages which are also generated at the connections. (cold junction compensation).
It is NOT possible to connect a thermocouple direct to a PICAXE and be able to read anything.