Hmmmm - I would guess that variances would present in a differential fashion, i.e. changing as a factor/percentage of the temperature.
A thermocouple's voltage is generated not at the tip, but in the wire itself - along the gradient of temperature change as it cools before reaching the cold-junction measurement located in the electronics of the probe hardware. My gut tells me it would be best to split wires as far from that gradient as possible - in other words, as far from the tip as possible. but - I'm sorry, I do not know this for sure. If you wanted to know how to write a programatic equation to measure that, I'm your man. But, on the electrical side of it - I think you'll find better sources of input than me.
An electrician might be a good idea - someone with some engineering knowledge.
If you were able to set up a call with Diedrich, I'd be happy to jump on the call with you. Let me know.