Thanks for mentioning calibration! You may get the question asked about the temperature from an auditor... How do you know that the temperature is correct? Perhaps it is a new digital type - it may still need to be "Verified" (Temperature on display is temperature in pot) at prescribed intervals with probes appropriate for the temperature.
The other issue and it may also fall under calibration / verification is the solder mixture. Most all solders are not 100% lead they are a mixture of lead (Pb) and Tin (Sn) typical would be a blend such as 63/37. 63% Tin and 37% Lead or 60/40 same principal. So, where this is going is when you first put solder in the pot most likely it is in balance (63/37) then as you use the pot and/or it is left heated up all day, certain metals burn off or get used up and the pot will end up out of balance. What this does is take us down another slippery slope... Now, how can you assure that what ever you are soldering is still acceptably soldered?
This now falls into the dreaded "Process Validation" definition.

I would suggest doing a full fledged IQ/OQ/PQ on the solder pot soldering process, including trials at different times like after pot is used for 1 week - will you still be soldering with the solder mixture you started with?
Just by looking you will not be able to tell unfortunately the solder is in balance. Based on risk and who the end customer is you may have to send out solder samples from the pot at various times to determine when it will go bad on you. Also this would be your process for calibration - seeing what the mixture is then making adjustments by adding Lead (Pb) or Tin (Sn) then testing until in balance. Other people find out how many hours/days/weeks before solder balance begins to drift then they just routinely just dump the whole pot and start all over with new solder.
*I used the example of leaded solder because of the simplicity, if you are using lead free solder like a SAC 305 you do not have (Pb) but you have 3 metals Sn, Ag, Cu. (More to keep in balance)
If you are lucky enough to have an XRF gun in house checking solder is quick and painless... You can send out solder samples to the solder manufacturer or if you are on the cheap go to a jewelry store or other place that buys gold, they often have an XRF gun and can shoot your solder sample maybe for free maybe for a few bucks.
So, between the temperature and the solder balance - Thinking that you can just plug in the solder pot add solder and you are all set is a huge misconception.

sorry for the epic book, perhaps it will help someone.