Thermocouple woes

Looking at the Wikipedia page on thermocouples I found this table:

Type	Temperature range °C (continuous)	Temperature range °C (short term)	Tolerance class one (°C)	Tolerance class two (°C)	IEC Color code	BS Color code	ANSI Color code
K	0 to +1100	−180 to +1300	±1.5 between −40 °C and 375 °C ±0.004×T between 375 °C and 1000 °C	±2.5 between −40 °C and 333 °C ±0.0075×T between 333 °C and 1200 °C
J	0 to +750	−180 to +800	±1.5 between −40 °C and 375 °C ±0.004×T between 375 °C and 750 °C	±2.5 between −40 °C and 333 °C ±0.0075×T between 333 °C and 750 °C
N	0 to +1100	−270 to +1300	±1.5 between −40 °C and 375 °C ±0.004×T between 375 °C and 1000 °C	±2.5 between −40 °C and 333 °C ±0.0075×T between 333 °C and 1200 °C
R	0 to +1600	−50 to +1700	±1.0 between 0 °C and 1100 °C ±[1 + 0.003×(T − 1100)] between 1100 °C and 1600 °C	±1.5 between 0 °C and 600 °C ±0.0025×T between 600 °C and 1600 °C			Not defined.
S	0 to 1600	−50 to +1750	±1.0 between 0 °C and 1100 °C ±[1 + 0.003×(T − 1100)] between 1100 °C and 1600 °C	±1.5 between 0 °C and 600 °C ±0.0025×T between 600 °C and 1600 °C			Not defined.
B	+200 to +1700	0 to +1820	Not Available	±0.0025×T between 600 °C and 1700 °C	No standard use copper wire	No standard use copper wire	Not defined.
T	−185 to +300	−250 to +400	±0.5 between −40 °C and 125 °C ±0.004×T between 125 °C and 350 °C	±1.0 between −40 °C and 133 °C ±0.0075×T between 133 °C and 350 °C
E	0 to +800	−40 to +900	±1.5 between −40 °C and 375 °C ±0.004×T between 375 °C and 800 °C	±2.5 between −40 °C and 333 °C ±0.0075×T between 333 °C and 900 °C
Chromel/AuFe	−272 to +300	n/a	Reproducibility 0.2% of the voltage; each sensor needs individual calibration.

I also had a closer look at the sheaths that the wires for the thermocouple are insulated with. The one going to the +ve port had red lines and the one to the -ve port had what appeared to be black lines in it. The background colour is white.

Based on that table then and if we assume the black is actually a very dark blue then the thermocouple used is most likely going to have been a K type which appear to be fairly popular so it should be easy to find a new one.

With 41 µV/°C I can calculate the maximum voltage I'll need to be able to spoof the thermocouple up to 600°C. I picked this as it shouldn't even go close but in case it does I can still test it.

With 3.3V avaliable from an old ATX PSU and (with some help from here) a voltage of 25.703mV(measuring 600°C reference 20°C) accross the thermocouple:

Voltage drop across fog machine=0.025703V

Voltage drop across resistors=3.274297V

Current flow from fog machine=V/R

                                                 =0.025703/1000 000

                                                 =0.000000026A

Resistance required=V/I

                               =3.274297/0.000000026

                               =125934500Ω

                               =125934.500kΩ

                               =125.934500MΩ

Which is pretty close to 126MΩ

However when I run this through KTechLab (Better than a SPICE simulator for a quick calculation) 10MΩ seems to be enough... perhaps I neglected to calculate current flow through the resistance array? I'll re-post once I have more info...