I dont think he has enough time to use thermocouples at all. Hes got like 9 or 10 days left till flight, and a buncha very good but terribly mismatched volunteer parts. Even if he had all chips and parts in hand with a proven design and pre-made circuit board for a compatible thermocouple amplifier, integrating an entire working payload system would be doubtful, even if they are very experienced.
Reminds me of an edge-of-space balloon flight, group project with what we though were modest goals. These were pretty experienced tinkerers, but night before launch everybody came to my basement lab with their assigned parts of the payload. Most were not working in themselves, much less integrated under a BasicStamp. By 0200 one guy and myself were left, we started from scratch, made a simple thermistor controlled 555 oscillator keying an oscillator from a VGA video card, 28.322 MHz = 10 m ham band. We spent the rest of the night calibrating it while trying to get FAA to accept our NOTAM filing. By 0900 everyone else was awake and joined us at launch site, the simple payload flew well to about 88000 ft (estimated from the NWS morning temperature profile) and was recovered less than 45 miles away.
BTW The guy who stayed awake all night with me is asleep in the back of the chase car. The guy in suspenders looks very familiar, I just dont recognize the old man who is in my mirror every morning ;-)
IMHO these folks dont need to be sitting up the night before the deadline trying to get help from this forum to debug unfamiliar circuits and new code. They need something Extremely Simple that has a decent chance of being a working and stable payload SEVERAL DAYS BEFORE the launch so they can get software thoroughly debugged and good ground experience in operating the system, triggering and downloading it, before the actual launch. Maybe even a test flight before going for the grade.
If it was me, sure, I'd be building a thermocouple amplifier, but even with my experience I'd already have those simple thermistors working just in case the deadline arrives "too sooon" .
MY $0.02 with no disrespect to the ideas of others. To borrow westfw's byline "Strongly opinionated, but not official!"
BTW, the one thing that NONE of us has yet helped Tetrahyde with is how to log (STORE) the data. The Dataq "logger" is just an Analog to RS-232 converter, they are fun but not really helpful here. If the data isnt sent down by telemetry and recorded then it gotta be stored onboard. Arduino has little memory, maybe a scheme to start storage on ignition and run till memory is full.... some of you may know sketches that can be adapted. Trigger could be electric igniter voltage or a break wire on rocket movement.