Hi Koch!
I had to mess with this same issue quite a bit in Beersmith. I have an SSBrewTech MT that is double walled SS with insulation inbetween (think yeti cup). I had to simply adjust this through trial and error, but mine came out to be .18.
There is, however a more scientific way to go about this that I learned in my chemistry class.
Weigh your vessel empty, write this down.
Fill with 2.5 gallons cold water, weigh this, subtract the difference of the vessel, this is the weight of the water ( use metric weight)… Water weighs 1g/ml or 1kg/L.
In a separate vessel, pour another 2.5gallons and record it’s weight as well. Begin heating this water to 80*C. (Being accurate with all measurements is important).
Meanwhile, place an accurate (to .01*C) thermometer in your kettle and record it’s temperature. Record the initial temperature of water, stir gently, record a temp reading every minute for 4 minutes. On the fifth minute it should have balanced out.
When your hot water is ready, pour it into the cold water and watch your thermometer. Stir, cover, record temp quickly.
Record temp every 30 sec for 5 minutes.
In Excel or another spreadsheet program, enter the time as your x-value and temp as your y-value and create a graph. Use the best fit option for a line overlay. This is only the data from the time you added your hot water to the calorimeter (kettle in your case).
Take the final temperature (temp at time 5mins) and subtract the initial temp from the final temp. Multiply this number by the mass of the cold water and 4.184 to find the amount of energy gained by the cold water in Joules.
Finally subtract the energy gained by the cold water from the energy lost by the hot water, this is the energy absorbed by the calorimeter (kettle) then divide the energy gained by the kettle by the change in temperature, this is the calorimeter constant for your kettle that you will use in BeerSmith.
Hope this helps, I had to refresh myself on this myself, here’s a website that I got the info from.