Did a search on the forums here and of the posts asking about thermocouples, no one else who was using the MKR Therm shield seemed to be complaining of the same issue.
To start, here are the components I'm using:
Arduino MKR Wifi 1010
MKR Therm Shield plugged in over the top of the MKR
Adafruit thermocouple - Thermocouple Type-K Glass Braid Insulated Stainless Steel Tip : ID 3245 : $9.95 : Adafruit Industries, Unique & fun DIY electronics and kits
To eliminate any sources of it being my fault through faulty programming, I'm just running the code at the bottom of https://www.arduino.cc/en/Guide/MKRTHERMShield
As far as I can tell, the Therm shield is seated correctly and I'm using the right libraries because the reference temp it prints to the console makes perfect sense for the temperature of my room. (About 73-ish F when I convert from C which is close to what I've set the home thermostat to)
But my thermocouple temp reads as 1073741824.00 °C. Over at reddit someone commented this is 100 0000 0000 0000 0000 0000 0000 0000 binary - so maybe an error code?
The thermocouple comes from Adafruit with maybe 1/8-1/4" wire exposed which isn't enough to reach into the inputs for the THERM shield, so I removed the shrink wrap at the end and exposed more wire. Still get similar readings.
I tried many times and mostly get that number. For maybe 1 minute I was able to get it to read about 10°C less than the room temp, but then it went back to 1073741824.00 °C.
Because the fiberglass was frayed when I got the thermocouple, I asked for a replacement from Aadafruit and the replacement displays the same behavior. So (possibly) not a hardware issue?
I ordered a new thermocouple from Amazon that comes wired with a K-type ending and I'll be able to try that today, so I don't know if that'll fix the issue when I can just plug it straight into the K-input on the board.
Just to reiterate my settings in case there's something easy and silly I've missed - this is the second Arduino/shield combo I've ever used. And just like my previous experience I just took the THERM board and made sure that the writing on the black connectors matched w/ the MKR board and just inserted the board's "feet" into the same black connectors on the MKR board. I didn't connect anything else (besides the thermocouple, of course). So if there are any additional things I need to connect - I don't know about them.
Thanks for any help!