Surface contact thermometer?
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Is there a thermometer or thermocouple that can accurately measure the nozzle temperature by just touching it to the nozzle?
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Best bet for accuracy would be starting with a 4 wire PT100 in the block.
Second best might be a thermocouple probe on your multimeter, but any contact sensor is going to bleed some heat away and will be generally poor contact pressure compared to the sensor in the block.
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I would add that it's the temperature of the filament inside the nozzle that is important, and that taking the measuring of the outside of the nozzle is probably the worse place. A while back I did some work to assess the affect of deflected part cooling air on the temperature inside a nozzle and saw temperature drops of up to 20 deg C with a steel nozzle. https://somei3deas.wordpress.com/2020/05/21/the-effect-of-deflected-part-cooling-air-on-brass-and-steel-nozzle-temperatures/
I dread to think what the measured temperature on the outside of the nozzle have been.