Max. Thermowell diameter

Im in the process of making thermowells for my Brutus (original Brutus uses dip tubes). Temp probe is 6mm, copper tubing with the closest I/D I can find is 10mm - is this too large ?
Im concerned that the probe will take too long to adjust to changes in temperature.
Also can someone suggest a good way to close the end of the tube ? I was considering simply flattening it in a vice - would this work ? I can't find end caps.

Crimp and solder them shut.

The probe will be touching the end when you insert it.

Thermal grease would help.

Great idea on the thermal grease - thanks.