Ha, I also used ice water as an experiment when road-testing the Pico Datalogger with k-type thermocouples. It was far from constant, but all in plausible range. I did not think about stirring, but noticed when the probe touches an ice cub it gets colder.
Yes, it was insulated but I did not put a lid on to make it a completely separated environment from ambient. I figured, the cold air on top of the water would stay there as it is heavier than warmer air.
As long as there is ice present and it stopped melting, the mixture should have settled at close to 0 degC, only exchanging energy with ambient through the glass and top.
PS: It is too warm on the Canadian east coast too, and humid.
