ScottG:
I don't think it's the wiring because it works fine with any one thermocouple hooked up. It's only when I have more then one T/C connected that I have a problem. To answer your question, I have the breakout board in the head of the thermocouple connected directly the the T/C probe wires. I have an unshielded 5 conductor 18 gauge stranded cable running between breakout board an Arduino. Cable is about 10 feet long.
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How do you have the 3 breakout boards wired to the Arduino?
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What code are you using?
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Is your thermocouple electrically isolated from the motor housing it is on? If it isn't, then you will pick up ground noise from the motor.