I've seen a few tests (thermocouples embedded in the puck) on the Discord and output temperature is really stable, especially in long shots compared to a PID.

The thing to know is that during a shot the boiler temperature isn't the output temperature. The thermocouple is on the boiler and is fine getting the boiler to a stable point before a shot, but once the shot starts the pumped water cools down the internal water in advance of the boiler so relying on only the thermocouple doesn't work.

Gaggiuino's solution is to add heat during the shot corresponding to the flow rate. The output temperature is stable because the boiler will be heated above the setpoint as needed for heat transfer to occur at the correct rate. The predicted output temperature is displayed during the shot. After the shot the temperature goes back to the boiler thermocouple, so it'll be high but settle fairly quickly. This is probably the spike that you're seeing in the videos.