I do not know about Archimedes. J. P. Joule invented the modern version. However, while the problem you cite is real, EVERYONE KNOWS ABOUT IT. Everyone who uses that kind of calorimeter does not measure at a single point, and they make sure they get a correctly averaged temperature that is accurate for the entire cell. They always discuss this in the papers. They always tell the reader how and why they are sure the temperature is averaged. There are many different methods. F&P used an array of sensors, and they made sure the electrolyte was well mixed with various tests. Miles put a copper sleeve around the cell and measured externally at several points in the copper. Copper conducts heat well, so the temperature was uniform, but he made sure it was.
In contrast to this, putting a single thermocouple on Mizuno's cell will definitely give you the wrong answer. He said that. He showed that in the figure we added to the Supplement. That's why we added it -- to send that message. This is the wrong approach. I have stated here several times, you cannot use the cell temperature to do calorimetery. On the other hand, you can use it to confirm there is excess heat. During a 50 W calibration it is ~30 deg C. During a 50 W input excess heat run it is ~350 deg C. That's a big difference. That cannot be a mistake. That definitely indicates excess heat. But you cannot use that number to estimate how much heat there is, except within a broad range. It gives a large overestimate.
I will add copper to the design.
