Thermocouple Amp is an AD8495
here's a photo of the setup

Wawa:
Returned A/D value depends on the analogue input and Aref.
Default Aref is the 5volt supply, and that is indeed a schottky diode drop lower on the Nano.
Lower Aref is higher A/D value (with the same analogue input voltage).
Bad practice to use default Aref for accurate temp (or other) measurements.
It's never quite the same, and so it the temp readout.
Better to use the internal 1.1volt bandgap Aref for stable measurements.
analogReference() - Arduino Reference
That value varies from Arduino to Arduino, but at least it's stable and independent of supply.
I also use a global variable for that, and write it on the Arduino board.
You might have to drop your sensor output to 0-1.1volt with a voltage divider.
Leo..
outsider:
The Nano has a blocking diode in the power supply that drops the voltage about 0.3 volts, test your AREF pin with an accurate DMM and change the (5.0 * reading) to match.
I always make a global float variable like:
float aRef = 4.82;
change it to suit whichever board I'm programming and use that instead of the 5.0, like:
float Vin = ( aRef * reading ) / 1024.0;
What you are saying is that by using 5V in my calculation inside the code, but the amp receiving less than 5V from the nano is messing up the reading, and I should use a reference voltage as a variable instead?
Is there a way to read the actual voltage coming from the board and use this? I'm worried that once this system becomes battery powered that voltage will drop, and this issue will arise again.
Koepel:
The picture of the output does not match the sketch you gave, because it uses the section that is commented out.
Can you rewrite the sketch and show it to us ? and show us the schematic and your wiring as MorganS wrote.
I assure you, the sketch I uploaded was the one used to take the screenshots, the commented out section was commented out to troubleshoot this issue. I will re-work the sketch now, I wanted to use PORTD to help avoid confusion as to what pins are on and off, and save some time. Currently this is only using two output pins, so digitalWrite() wouldn't be hard to replace it with, however once it works we will be using 4 or 5 outputs.